CBSE Class 7 Mathematics Comparing Quantities Worksheet Set 03

Question. In a village, 30% people are women, 40% are men rest are Children what is the % of children in the village.

Question. Convert 45% into fraction.
(A) 8/20
(B) 7/10
(C) 9/20
(D) 9/10

Question. Write 3/4 in the form of percentage?
(A) 60%
(B) 45%
(C) 75%
(D) 40%

Question. Out of 80 students in a class 30 are girls. Find the percentage of girls in class.
(A) 40%
(B) 30%
(C) 45%
(D) 37.5%

Question. Convert 540/400 into decimals
(A) 1.45
(B) 1.30
(C) 1.35
(D) 1.67

Question. Ιn a city, 25% are females, 45% are males and remaining are children. What is the percentage of children?
(A) 30%
(B) 20%
(C) 40%
(D) 25%

Question. If 75% of students in a class have a bicycle, what percent of the student do not have bicycles?
(A) 25%
(B) 35%
(C) 40%
(D) 30%

Question. The cost of 9 bowls is Rs 72. Find the cost of 6 such bowls.
(A) Rs 50
(B) Rs 60
(C) Rs 70
(D) Rs 48

Question. Calculate the following
i) 12% of 120
ii) 30% of 300

Question. The weight of one iron ball is 16kg. Find the weight of 8 such iron balls.
(A) 100 kg
(B) 250 kg
(C) 128 kg
(D) 160 kg

Question. The ratio of 5 m and 150 cm is ……..
(A) 3:10
(B) 10:3
(C) 3:11
(D) 11:3

Question. Convert 4:1 into percentage.
(A) 80%:20%
(B) 75%:25%
(C) 60%:40%
(D) 20%:80%

Question. A shopkeeper bought a chair for Rs 375 and sold it for Rs 400. Find the gain percentage.
(A) 5
(B) 3
(C) 4
(D) 6

Question. Price of shirt decreased from Rs 80 to 60. Find the percentage of decreased price?
(A) 25%
(B) 30%
(C) 40%
(D) 45%

Question. Ιn the given figure, find the per cent which is colored?
(A) 25%
(B) 50%
(C) 75%
(D) 30%

Question. What will be the correct sign come between 2/3 and 1/5 ?
(A) =
(B) >
(C) <
(D) ≈

Question. The cost of 8 bowls is Rs 48. What would be the cost of 5 such bowls?
(A) Rs 36
(B) Rs 39
(C) Rs 30
(D) Rs 24

Question. A basket is full of fruits mangoes, oranges and apples. If 60% are mangoes, 10% are oranges than what is the percentage of apples.

Question. Neelu got 320/400 in her report card. Hari scored 280/400 in his report card. Who scored more percentage of marks?
(A) Neelu
(B) Hari
(C) Ratios cannot be compared
(D) Can't say

Question. There are 25 radios. 16 of them are damaged. Find the percentage of damaged radios.
(A) 60%
(B) 45%
(C) 64%
(D) 80%

Question. The number of illiterate persons in a country decreased from 150 lakhs to 100 lakhs in 10 yrs. What is the decrease percentage?
(A) 33.3%
(B) 40%
(C) 70%
(D) 90%

Question. In a survey of 40 students, 25% of students liked to play football. What is the number of students who like to play football?
(A) 10
(B) 20
(C) 25
(D) 5

Question. Are the two ratios equal? 2/5 and 3/8
(A) Yes
(B) No
(C) Might be
(D) Can't say

Question. Find the ratio of 40 days to 40 hrs.
(A) 24:1
(B) 30:7
(C) 48:1
(D) 13:2

Question. Out of 80 students in a class 30 are girls. Find the percentage of girls in class.
(A) 40%
(B) 30%
(C) 45%
(D) 37.5%

Question. The population of Rajasthan is 570 lakh and population of U.P is 1,560 lakh in the same area. Find the ratio of their population.
(A) 20:23
(B) 33:11
(C) 19:52
(D) 19:62

Question. Find the whole quantity if 5% of it is 600.
(A) 12,000
(B) 11,000
(C) 1,000
(D) 15,000

Question. Out of 40 students, 8 are absent. What per cent of the students are absent?
(A) 30%
(B) 20%
(C) 25%
(D) 35%

Question. Find 2% of 1hr .
(A) 70 sec
(B) 72 sec
(C) 80 sec
(D) 100 sec

Question. Convert into percentage.
i. 1/3 = ----%
ii. 1/6 = ----%

Question. Convert 33% into decimals
(A) 0.33
(B) 3.3
(C) 330
(D) 0.033

Question. 35% + ? % = 100%
(A) 60%
(B) 65%
(C) 45%
(D) 75%

Question. Convert 0.45 into percentage.
(A) 450%
(B) 4,500%
(C) 4.5%
(D) 45%

Question. Define Unitary Method.
(A) First we find the value of the required number of units and then the value of one unit.
(B) First we find the value of 10 units and then the value of one unit.
(C) First we find the value of one unit and then the value of the required units.
(D) None of them

Question. Find the ratio of Rs 500 to 50,000 paise.
(A) 1:1
(B) 2:1
(C) 4:1
(D) 10:1

Question. What percentage of the figure is shaded?
(A) 30%
(B) 25%
(C) 44%
(D) 54%

Question. There are 110 votes, 77 of them voted yes. What per cent of voted no?
(A) 40%
(B) 30%
(C) 20%
(D) 25%

Question. The buying price of any item is known as it's …………
(A) Selling price
(B) Cost price
(C) Marked price
(D) Profit

Question. An article was sold for Rs 330 with a profit 10%. What was its cost price?
(A) Rs 300
(B) Rs 310
(C) Rs 275
(D) Rs 250

Question. I = (PR......)/100, where P is Principal, R is rate of interest and I is simple interest.
(A) M
(B) T
(C) N
(D) None of them

Question. Find the value of x, if 64% + 30% + x = 100%.
(A) 5%
(B) 6%
(C) 4%
(D) 7%

Question. Convert 0.03 into percentage.
(A) 3%
(B) 30%
(C) 0.3%
(D) None of them

Question. Convert into per cent
(A) 72 %
(B) 76 %
(C) 78 %
(D) 80 %

Question. Convert 25% into fraction.
(A) 1/4
(B) 1/3
(C) 2/3
(D) 3/2

Question. Find out the numbers if
i. 10% of number is 600
ii. 12% of number is 1080

Question. If P = Rs 1200 at 12% per annum and T = 3, then find interest.
(A) Rs 430
(B) Rs 432
(C) Rs 288
(D) Rs 576

Question. What rate gives Rs 280 as interest on a sum of Rs 56,000 in 2 years?
(A) 0.5%
(B) 0.25%
(C) 2.5%
(D) 0.05%

Question. Cost of an item is Rs 25. It was sold with a profit of 12%. What was the selling price?
(A) Rs 32
(B) Rs 28
(C) Rs 27
(D) Rs 30

Question. An item was sold for Rs 540, if the cost price of its item is Rs 600. What is the loss percentage?
(A) 12%
(B) 10%
(C) 15%
(D) 20%

Question. The cost of 13 books is Rs 299. What would be the cost of 3 books?
(A) Rs 46
(B) Rs 69
(C) Rs 92
(D) Rs 96

Question. Convert the following into fraction and Decimal
i) 24 1/2 %
ii) 39.2%

Question. Find the ratio of
i.1m to 1 Km.
ii.1 week of Feb. to Feb. month

Question. If angles of a triangle are in the ratio 2:3:4. What is the value of greatest angle?
(A) 40°
(B) 60°
(C) 80°
(D) 50°

Question. The cost of a flower vase is Rs 120. If the shopkeeper sells it at a loss of 10%, find the Selling price
(A) Rs 110
(B) Rs 108
(C) Rs 112
(D) Rs 132

Question. Find the amount to be paid at the end of 3 yrs if the principal amount is Rs 1,200 at 10%p.a.
(A) Rs 1,300
(B) Rs 1,560
(C) Rs 1,498
(D) Rs 1360

Question. Find the simple interest that Ram has to pay if he borrows Rs 500 for a period of 5 yrs at the rate of 5% p.a.
(A) Rs 200
(B) Rs 150
(C) Rs 100
(D) Rs 125

Question. Selling price of a toy is Rs 540. If the profit made by the shopkeeper is 20%, find the cost price of the toy.
(A) Rs 500
(B) Rs 450
(C) Rs 520
(D) Rs 600

Question. Total numbers of beads in a bag are 20, if red beads are 8 and blue beads are 12, find out the percentage of each colour of beads.

Question. The cost of one packet of balls having 20 balls is Rs. 100, what will be the cost of such 24 balls.

Question. Amina buys a book for Rs 275 and sells it at loss of 15%. How much does she sell it for?
(A) Rs 233.50
(B) Rs 233.75
(C) Rs 233.25
(D) Rs 240.00

Question. A man buys 3 oranges for Rs. 4 and sells 4 oranges for Rs. 6. Find his Gain or loss percent.

Question. A shopkeeper is selling an article of Rs.400, while he purchases it for Rs. 402. Find out loss percent of shopkeeper.

Question. One person divides his income in two parts if he gives 2 parts to Ram and 1 part to Shyam. What percentage of money he gives to Ram and Shyam separately.

Question. Angles of a quadrilateral are in ratio 2 : 3 : 3 : 4, find out all the angles of quadrilateral.

Question. The loss in a company has decreased from 20 lacs to 5 lacs in one year. Find the loss decrease percentage.

Question. Out of 30 students in a hostel, 8 are goingto market, 20 are going to watching T.V, rest of the students are studying. Convert all of them into percentage.

Question. Find the whole quantity if
(a) 12% of it is Rs 1080
(b) 40% of it is 500 km

Question. Find the simple interest on Rs. 1200 from 2006 to 2009 at 6% per annum and also find the amount to be paid at the end of 3 years.

Question. A man purchase two machines at Rs. 1200 each. On one he gain 20% and on the other he loses 20%. How much does he gain or lose in whole transaction.

Question. A farmer borrowed Rs 5000 from a money lender at 9% per annum. After 4 years, he cleared the account by giving Rs 5500 and a cow to the money lender. Find the cost of the cow.

Question. Calculate the principle when
(i) Amount = Rs 4637.50 and simple interest = Rs 1137.50
(ii) Amount = Rs 10000 and simple interest = Rs 3750
(iii) Amount = Rs 7539 and simple interest = Rs 1523
(iv) What rates gives Rs 280 as interest on a sum of 56,000 in 2 years?

Question. 9900 students of Chennai appeared in the board examination. Out of them 35% secured 1st division, 45% secured 2nd division, 10% were allowed for compartmental examination and the rest failed. Find out the number of students in each category.

Question. An article was sold for Rs 250 with a profit of 5%. What was its cost price?

Comparing Quantities

1 Mark Questions

Question 1. In a village, 30% people are women, 40% are men rest are Children what is the % of children in the village.
Answer: The total population of the village represents 100%.
Percentage of adults = \( 30\% + 40\% = 70\% \).
Percentage of children = \( 100\% - 70\% = 30\% \).
Therefore, the percentage of children in the village is 30%.
In simple words: Add the men and women together to get 70%. Take 70% away from 100% to find that 30% are children.

Exam Tip: Remember that all groups in a whole population always add up to 100%.

Question 2. Convert 45% into fraction.
(a) 8/20
(b) 7/10
(c) 9/20
(d) 9/10
Answer: (c) 9/20
To change a percentage into a fraction, divide by 100 and simplify:
\( 45\% = \frac{45}{100} \)
Divide both numerator and denominator by 5:
\( \frac{45 \div 5}{100 \div 5} = \frac{9}{20} \).
In simple words: Write 45 over 100 and divide top and bottom by 5 to get 9/20.

Exam Tip: Always reduce the fraction to its lowest terms by finding the highest common factor.

Question 3. Write 3/4 in the form of percentage?
(a) 60%
(b) 45%
(c) 75%
(d) 40%
Answer: (c) 75%
To convert a fraction into a percentage, multiply by 100%:
\( \frac{3}{4} \times 100\% = 3 \times 25\% = 75\% \).
In simple words: Multiply 3/4 by 100 to get 75%.

Exam Tip: Multiplying any fraction by 100 immediately changes it into a percentage.

Question 4. Out of 80 students in a class 30 are girls. Find the percentage of girls in class.
(a) 40%
(b) 30%
(c) 45%
(d) 37.5%
Answer: (d) 37.5%
Total students = 80.
Number of girls = 30.
Percentage of girls:
\( \frac{30}{80} \times 100\% = \frac{3}{8} \times 100\% = \frac{300}{8}\% = 37.5\% \).
In simple words: Divide 30 girls by 80 total students and multiply by 100 to get 37.5%.

Exam Tip: Remember that \( \frac{1}{8} = 12.5\% \), so \( \frac{3}{8} = 3 \times 12.5\% = 37.5\% \).

Question 5. Convert 540/400 into decimals
(a) 1.45
(b) 1.30
(c) 1.35
(d) 1.67
Answer: (c) 1.35
Cancel the common zero in numerator and denominator:
\( \frac{540}{400} = \frac{54}{40} \)
Divide numerator and denominator by 2:
\( \frac{27}{20} = \frac{27 \times 5}{20 \times 5} = \frac{135}{100} = 1.35 \).
In simple words: Simplify the fraction to 27/20, then make the bottom 100 to get 1.35.

Exam Tip: Convert denominators like 20, 25, or 50 into 100 to write decimals quickly without long division.

Question 6. Ιn a city, 25% are females, 45% are males and remaining are children. What is the percentage of children?
(a) 30%
(b) 20%
(c) 40%
(d) 25%
Answer: (a) 30%
Total population percentage = 100%.
Sum of females and males = \( 25\% + 45\% = 70\% \).
Percentage of children = \( 100\% - 70\% = 30\% \).
In simple words: Add 25% and 45% to get 70%. Subtract 70% from 100% to leave 30% children.

Exam Tip: Check your subtraction carefully: 100 minus 70 leaves 30.

Question 7. If 75% of students in a class have a bicycle, what percent of the student do not have bicycles?
(a) 25%
(b) 35%
(c) 40%
(d) 30%
Answer: (a) 25%
The whole class equals 100%.
Percentage without bicycles = \( 100\% - 75\% = 25\% \).
In simple words: Take 75% away from 100% to get 25%.

Exam Tip: Questions asking "what percent do not" simply require subtracting the given percentage from 100%.

Question 8. The cost of 9 bowls is Rs 72. Find the cost of 6 such bowls.
(a) Rs 50
(b) Rs 60
(c) Rs 70
(d) Rs 48
Answer: (d) Rs 48
Using unitary method:
Cost of 1 bowl = \( \frac{72}{9} = \text{Rs } 8 \).
Cost of 6 bowls = \( 6 \times 8 = \text{Rs } 48 \).
In simple words: One bowl costs Rs 8. So 6 bowls cost 6 times 8, which is Rs 48.

Exam Tip: First calculate the cost of one single item before multiplying by the required number of items.

Question 9. Calculate the following
(i) 12% of 120
(ii) 30% of 300
Answer:
(i) \( 12\% \text{ of } 120 = \frac{12}{100} \times 120 = \frac{1440}{100} = 14.4 \).
(ii) \( 30\% \text{ of } 300 = \frac{30}{100} \times 300 = 30 \times 3 = 90 \).
In simple words: Multiply each percentage fraction by the given number to find the value.

Exam Tip: In part (ii), cancel two zeroes from 100 and 300 directly to make the multiplication simple.

Question 10. The weight of one iron ball is 16kg. Find the weight of 8 such iron balls.
(a) 100 kg
(b) 250 kg
(c) 128 kg
(d) 160 kg
Answer: (c) 128 kg
Weight of 1 ball = 16 kg.
Weight of 8 balls = \( 16 \times 8 = 128\text{ kg} \).
In simple words: Multiply 16 kg by 8 to get a total weight of 128 kg.

Exam Tip: Always remember to write the units (kg) alongside the final numerical value.

Question 11. The ratio of 5 m and 150 cm is ……..
(a) 3:10
(b) 10:3
(c) 3:11
(d) 11:3
Answer: (b) 10:3
First convert metres into centimetres:
\( 5\text{ m} = 5 \times 100\text{ cm} = 500\text{ cm} \).
Now write the ratio:
\( \frac{500}{150} = \frac{50}{15} = \frac{10}{3} = 10:3 \).
In simple words: Change 5 m into 500 cm. The ratio 500 to 150 simplifies to 10:3.

Exam Tip: Both quantities must have the same unit before forming a ratio.

Question 12. Convert 4:1 into percentage.
(a) 80%:20%
(b) 75%:25%
(c) 60%:40%
(d) 20%:80%
Answer: (a) 80%:20%
Total number of parts = \( 4 + 1 = 5 \).
First part percentage = \( \frac{4}{5} \times 100\% = 80\% \).
Second part percentage = \( \frac{1}{5} \times 100\% = 20\% \).
Therefore, the ratio in percentage is 80%:20%.
In simple words: The total is 5 parts. 4 out of 5 is 80% and 1 out of 5 is 20%.

Exam Tip: Find the sum of the ratio parts first to use as the denominator.

Question 13. A shopkeeper bought a chair for Rs 375 and sold it for Rs 400. Find the gain percentage.
(a) \( 5\frac{2}{3}\% \)
(b) \( 3\frac{2}{3}\% \)
(c) \( 4\frac{2}{3}\% \)
(d) \( 6\frac{2}{3}\% \)
Answer: (d) 6 2/3%
Cost Price (CP) = Rs 375.
Selling Price (SP) = Rs 400.
Gain = \( 400 - 375 = \text{Rs } 25 \).
Gain percentage = \( \frac{\text{Gain}}{\text{CP}} \times 100\% \)
\( = \frac{25}{375} \times 100\% = \frac{1}{15} \times 100\% = \frac{20}{3}\% = 6\frac{2}{3}\% \).
In simple words: The profit is Rs 25. Divide 25 by the cost price 375 and multiply by 100 to get 6 2/3%.

Exam Tip: Gain percentage is always calculated using the Cost Price in the denominator.

Question 14. Price of shirt decreased from Rs 80 to 60. Find the percentage of decreased price?
(a) 25%
(b) 30%
(c) 40%
(d) 45%
Answer: (a) 25%
Original price = Rs 80.
Decrease in price = \( 80 - 60 = \text{Rs } 20 \).
Percentage decrease = \( \frac{\text{Decrease}}{\text{Original Price}} \times 100\% \)
\( = \frac{20}{80} \times 100\% = \frac{1}{4} \times 100\% = 25\% \).
In simple words: The price dropped by Rs 20. Divide 20 by the original Rs 80 to get 25%.

Exam Tip: Always divide the decrease by the initial price, not the reduced price.

Question 15. Ιn the given figure, find the per cent which is colored?
(a) 25%
(b) 50%
(c) 75%
(d) 30%
Answer: (a) 25%
The square is divided into 4 equal triangular parts.
Number of colored parts = 1.
Fraction colored = \( \frac{1}{4} \).
Percentage colored = \( \frac{1}{4} \times 100\% = 25\% \).
In simple words: 1 part out of 4 equal parts is shaded, which equals 25%.

Exam Tip: Count the total number of identical parts first to find the denominator.

Question 16. What will be the correct sign come between 2/3 and 1/5 ?
(a) =
(b) >
(c) <
(d) None of the options
Answer: (b) >
Compare \( \frac{2}{3} \) and \( \frac{1}{5} \) by cross-multiplying:
\( 2 \times 5 = 10 \) and \( 1 \times 3 = 3 \).
Since \( 10 > 3 \), it follows that \( \frac{2}{3} > \frac{1}{5} \).
In simple words: 2/3 is about 0.67 and 1/5 is 0.20, so 2/3 is greater.

Exam Tip: Use cross-multiplication (\( 2 \times 5 \) vs \( 3 \times 1 \)) to compare fractions quickly without finding a common denominator.

Question 17. The cost of 8 bowls is Rs 48. What would be the cost of 5 such bowls?
(a) Rs 36
(b) Rs 39
(c) Rs 30
(d) Rs 24
Answer: (c) Rs 30
Cost of 1 bowl = \( \frac{48}{8} = \text{Rs } 6 \).
Cost of 5 bowls = \( 5 \times 6 = \text{Rs } 30 \).
In simple words: One bowl costs Rs 6, so five bowls cost Rs 30.

Exam Tip: Find the unit price first, then multiply by the required quantity.

Question 18. A basket is full of fruits mangoes, oranges and apples. If 60% are mangoes, 10% are oranges than what is the percentage of apples.
Answer: Total percentage of fruits in the basket = 100%.
Percentage of mangoes and oranges = \( 60\% + 10\% = 70\% \).
Percentage of apples = \( 100\% - 70\% = 30\% \).
Therefore, the percentage of apples is 30%.
In simple words: Add mangoes and oranges to get 70%. Subtract from 100% to find that 30% are apples.

Exam Tip: Sum all given percentages and subtract from 100% to find the missing category.

Question 19. Neelu got 320/400 in her report card. Hari scored 280/400 in his report card. Who scored more percentage of marks?
(a) Neelu
(b) Hari
(c) Ratios cannot be compared
(d) Can't say
Answer: (a) Neelu
Neelu's percentage = \( \frac{320}{400} \times 100\% = \frac{320}{4}\% = 80\% \).
Hari's percentage = \( \frac{280}{400} \times 100\% = \frac{280}{4}\% = 70\% \).
Since 80% > 70%, Neelu scored a higher percentage.
In simple words: Neelu scored 80% and Hari scored 70%, so Neelu scored higher.

Exam Tip: When total marks are the same, the student with the higher score always has the higher percentage.

Question 20. There are 25 radios. 16 of them are damaged. Find the percentage of damaged radios.
(a) 60%
(b) 45%
(c) 64%
(d) 80%
Answer: (c) 64%
Total radios = 25.
Damaged radios = 16.
Percentage damaged = \( \frac{16}{25} \times 100\% = 16 \times 4\% = 64\% \).
In simple words: Divide 16 by 25 and multiply by 100 to get 64%.

Exam Tip: Multiply the numerator by 4 when the denominator is 25 to find the percentage quickly.

Question 21. The number of illiterate persons in a country decreased from 150 lakhs to 100 lakhs in 10 yrs. What is the decrease percentage?
(a) 33.3%
(b) 40%
(c) 70%
(d) 90%
Answer: (a) 33.3%
Original number = 150 lakhs.
Decrease in number = \( 150 - 100 = 50\text{ lakhs} \).
Percentage decrease = \( \frac{50}{150} \times 100\% = \frac{1}{3} \times 100\% = 33.33\% \approx 33.3\% \).
In simple words: The count fell by 50 lakhs out of 150 lakhs, which is a drop of one-third or 33.3%.

Exam Tip: The timeframe of 10 years is extra details; calculate the percentage decrease using only the initial and final values.

Question 22. In a survey of 40 students, 25% of students liked to play football. What is the number of students who like to play football?
(a) 10
(b) 20
(c) 25
(d) 5
Answer: (a) 10
Total students = 40.
Number of students who like football = \( 25\% \text{ of } 40 = \frac{25}{100} \times 40 = \frac{1}{4} \times 40 = 10 \).
In simple words: 25% is one-fourth. One-fourth of 40 students is 10 students.

Exam Tip: Use 25% = 1/4 to find one-fourth of any number directly.

Question 23. Are the two ratios equal? 2/5 and 3/8
(a) Yes
(b) No
(c) Might be
(d) Can't say
Answer: (b) No
Cross-multiply the two fractions:
\( 2 \times 8 = 16 \)
\( 3 \times 5 = 15 \)
Since \( 16 \neq 15 \), the two ratios \( \frac{2}{5} \) and \( \frac{3}{8} \) are not equal.
In simple words: Cross-multiplying gives 16 and 15. Because these numbers are different, the ratios are not equal.

Exam Tip: Two ratios a/b and c/d are equal only if their cross-products a × d and b × c are identical.

Question 24. Find the ratio of 40 days to 40 hrs.
(a) 24:1
(b) 30:7
(c) 48:1
(d) 13:2
Answer: (a) 24:1
Convert days to hours (1 day = 24 hours):
\( 40\text{ days} = 40 \times 24\text{ hours} = 960\text{ hours} \).
Ratio = \( \frac{960}{40} = \frac{24}{1} = 24:1 \).
In simple words: 40 days has 24 times as many hours as 40 hours, so the ratio is 24:1.

Exam Tip: Always convert both terms to the smaller unit before calculating the ratio.

Question 25. Out of 80 students in a class 30 are girls. Find the percentage of girls in class.
(a) 40%
(b) 30%
(c) 45%
(d) 37.5%
Answer: (d) 37.5%
Percentage of girls = \( \frac{30}{80} \times 100\% = \frac{3}{8} \times 100\% = 37.5\% \).
In simple words: 30 out of 80 is 3/8, which equals 37.5%.

Exam Tip: Simplify the fraction 30/80 to 3/8 first, then multiply by 100.

Question 26. The population of Rajasthan is 570 lakh and population of U.P is 1,560 lakh in the same area. Find the ratio of their population.
(a) 20:23
(b) 33:11
(c) 19:52
(d) 19:62
Answer: (c) 19:52
Ratio = \( \frac{570}{1560} = \frac{57}{156} \).
Divide both numbers by 3:
\( \frac{57 \div 3}{156 \div 3} = \frac{19}{52} = 19:52 \).
In simple words: Cancel the zeroes to get 57/156, then divide both by 3 to reach 19:52.

Exam Tip: Check divisibility by 3: \( 5 + 7 = 12 \) and \( 1 + 5 + 6 = 12 \), so both numbers divide by 3.

Question 27. Find the whole quantity if 5% of it is 600.
(a) 12,000
(b) 11,000
(c) 1,000
(d) 15,000
Answer: (a) 12,000
Let the whole quantity be \( x \).
\( 5\% \text{ of } x = 600 \)
\( \frac{5}{100} \times x = 600 \)

\( \implies x = \frac{600 \times 100}{5} = 600 \times 20 = 12,000 \).
In simple words: Multiply 600 by 100 and divide by 5 to find the total quantity of 12,000.

Exam Tip: To find the whole from 5%, multiply the given value by 20.

Question 28. Out of 40 students, 8 are absent. What per cent of the students are absent?
(a) 30%
(b) 20%
(c) 25%
(d) 35%
Answer: (b) 20%
Percentage of absent students = \( \frac{8}{40} \times 100\% = \frac{1}{5} \times 100\% = 20\% \).
In simple words: 8 out of 40 simplifies to 1/5, which is 20%.

Exam Tip: Remember that \( \frac{1}{5} = 20\% \) to solve such questions in seconds.

Question 29. Find 2% of 1hr .
(a) 70 sec
(b) 72 sec
(c) 80 sec
(d) 100 sec
Answer: (b) 72 sec
Convert 1 hour into seconds:
\( 1\text{ hour} = 60 \times 60\text{ seconds} = 3600\text{ seconds} \).
\( 2\% \text{ of } 3600\text{ sec} = \frac{2}{100} \times 3600 = 2 \times 36 = 72\text{ seconds} \).
In simple words: 1 hour is 3600 seconds. 2% of 3600 is 72 seconds.

Exam Tip: Convert hours into seconds before calculating the percentage.

Question 30. Convert into percentage.
(i) 1/3 = ----%
(ii) 1/6 = ----%
Answer:
(i) \( \frac{1}{3} \times 100\% = \frac{100}{3}\% = 33\frac{1}{3}\% \) (or \( 33.33\% \)).
(ii) \( \frac{1}{6} \times 100\% = \frac{50}{3}\% = 16\frac{2}{3}\% \) (or \( 16.67\% \)).
In simple words: Multiply each fraction by 100 to get 33 1/3% and 16 2/3%.

Exam Tip: Writing the answers as mixed fractions (\( 33\frac{1}{3}\% \) and \( 16\frac{2}{3}\% \)) is more accurate than terminating decimals.

Question 31. Convert 33% into decimals
(a) 0.33
(b) 3.3
(c) 330
(d) 0.033
Answer: (a) 0.33
To change a percentage into a decimal, divide by 100:
\( 33\% = \frac{33}{100} = 0.33 \).
In simple words: Move the decimal point two places to the left to get 0.33.

Exam Tip: Dividing by 100 always moves the decimal point two digits to the left.

Question 32. 35% + ? % = 100%
(a) 60%
(b) 65%
(c) 45%
(d) 75%
Answer: (b) 65%
Missing percentage = \( 100\% - 35\% = 65\% \).
In simple words: 100 minus 35 gives 65%.

Exam Tip: Subtract the known percentage from 100% to find the missing value.

Question 33. Convert 0.45 into percentage.
(a) 450%
(b) 4,500%
(c) 4.5%
(d) 45%
Answer: (d) 45%
Multiply the decimal by 100%:
\( 0.45 \times 100\% = 45\% \).
In simple words: Shift the decimal point two places right to get 45%.

Exam Tip: Multiply decimals by 100 to convert them to percentages.

Question 34. Define Unitary Method.
(a) First we find the value of the required number of units and then the value of one unit.
(b) First we find the value of 10 units and then the value of one unit.
(c) First we find the value of one unit and then the value of the required units.
(d) None of them
Answer: (c) First we find the value of one unit and then the value of the required units.
The unitary method is a problem-solving technique where we determine the value of a single unit first, and then multiply to find the value of the desired quantity.
In simple words: Unitary method means finding the cost or value of one item first, then using that to find the cost of many items.

Exam Tip: The word "unitary" comes from "unit", meaning one single item.

Question 35. Find the ratio of Rs 500 to 50,000 paise.
(a) 1:1
(b) 2:1
(c) 4:1
(d) 10:1
Answer: (a) 1:1
Convert rupees to paise (Rs 1 = 100 paise):
\( \text{Rs } 500 = 500 \times 100\text{ paise} = 50,000\text{ paise} \).
Ratio = \( \frac{50,000}{50,000} = \frac{1}{1} = 1:1 \).
In simple words: Rs 500 equals 50,000 paise. Both amounts are equal, so the ratio is 1:1.

Exam Tip: Match the units before setting up your ratio.

Question 36. What percentage of the figure is shaded?
(a) 30%
(b) 25%
(c) 44%
(d) 54%
Answer: (b) 25%
The circle is divided into 8 equal sectors.
Number of shaded sectors = 2.
Fraction shaded = \( \frac{2}{8} = \frac{1}{4} \).
Percentage shaded = \( \frac{1}{4} \times 100\% = 25\% \).
In simple words: 2 out of 8 slices are shaded, which simplifies to 1/4 or 25%.

Exam Tip: Count all sections to form the denominator, then count shaded sections for the numerator.

Question 37. There are 110 votes, 77 of them voted yes. What per cent of voted no?
(a) 40%
(b) 30%
(c) 20%
(d) 25%
Answer: (b) 30%
Number of votes for "no" = \( 110 - 77 = 33 \).
Percentage of "no" votes = \( \frac{33}{110} \times 100\% = \frac{3}{10} \times 100\% = 30\% \).
In simple words: 33 people voted no. 33 divided by 110 times 100 gives 30%.

Exam Tip: First subtract to find the number of people who voted "no" before calculating the percentage.

Question 38. The buying price of any item is known as it's …………
(a) Selling price
(b) Cost price
(c) Marked price
(d) Profit
Answer: (b) Cost price
The price at which an article is purchased is called its Cost Price (CP).
In simple words: The amount paid to buy an item is its cost price.

Exam Tip: Selling price is the price at which goods are sold, while cost price is the buying price.

Question 39. An article was sold for Rs 330 with a profit 10%. What was its cost price?
(a) Rs 300
(b) Rs 310
(c) Rs 275
(d) Rs 250
Answer: (a) Rs 300
Selling Price (SP) = Rs 330, Profit = 10%.
\( \text{SP} = \text{CP} \times \frac{100 + \text{Profit}\%}{100} \)
\( 330 = \text{CP} \times \frac{110}{100} \)

\( \implies \text{CP} = \frac{330 \times 100}{110} = 3 \times 100 = \text{Rs } 300 \).
In simple words: Rs 330 is 110% of the cost price. Dividing 330 by 1.1 gives Rs 300.

Exam Tip: Avoid the trap of subtracting 10% of 330 from 330; profit percentage is always on cost price.

Question 40. I = (PR......)/100, where P is Principal, R is rate of interest and I is simple interest.
(a) M
(b) T
(c) N
(d) None of them
Answer: (b) T
The standard formula for simple interest is \( I = \frac{P \times R \times T}{100} \), where T represents Time in years.
In simple words: The letter T stands for time in the simple interest formula.

Exam Tip: Always make sure time T is expressed in years when using this formula.

Question 41. Find the value of x, if 64% + 30% + x = 100%.
(a) 5%
(b) 6%
(c) 4%
(d) 7%
Answer: (b) 6%
\( 64\% + 30\% + x = 100\% \)
\( 94\% + x = 100\% \)

\( \implies x = 100\% - 94\% = 6\% \).
In simple words: 64 plus 30 is 94. 100 minus 94 gives 6%.

Exam Tip: Add the given percentages together first, then subtract from 100%.

Question 42. Convert 0.03 into percentage.
(a) 3%
(b) 30%
(c) 0.3%
(d) None of them
Answer: (a) 3%
\( 0.03 \times 100\% = 3\% \).
In simple words: Move the decimal point two places to the right to get 3%.

Exam Tip: Multiplying 0.03 by 100 shifts the decimal point past both digits, leaving 3.

Question 43. Convert 39/50 into per cent
(a) 72 %
(b) 76 %
(c) 78 %
(d) 80 %
Answer: (c) 78 %
Multiply the fraction by 100%:
\( \frac{39}{50} \times 100\% = 39 \times 2\% = 78\% \).
In simple words: 50 goes into 100 twice. 39 times 2 is 78%.

Exam Tip: When the denominator is 50, simply double the numerator to find the percentage.

Question 44. Convert 25% into fraction.
(a) 1/4
(b) 1/3
(c) 2/3
(d) 3/2
Answer: (a) 1/4
\( 25\% = \frac{25}{100} = \frac{1}{4} \).
In simple words: 25 divided by 100 reduces to 1/4.

Exam Tip: Divide numerator and denominator by 25 to simplify in one step.

2 Mark Questions

Question 45. Find out the numbers if
(i) 10% of number is 600
(ii) 12% of number is 1080
Answer:
(i) Let the number be \( x \):
\( 10\% \text{ of } x = 600 \)
\( \frac{10}{100} \times x = 600 \)

\( \implies x = \frac{600 \times 100}{10} = 6000 \).
(ii) Let the number be \( y \):
\( 12\% \text{ of } y = 1080 \)
\( \frac{12}{100} \times y = 1080 \)

\( \implies y = \frac{1080 \times 100}{12} = 90 \times 100 = 9000 \).
In simple words: Divide the given value by the percentage and multiply by 100 to find the original numbers, which are 6000 and 9000.

Exam Tip: Set up an equation with a variable like x to avoid calculation errors.

Question 46. If P = Rs 1200 at 12% per annum and T = 3, then find interest.
(a) Rs 430
(b) Rs 432
(c) Rs 288
(d) Rs 576
Answer: (b) Rs 432
\( \text{Simple Interest} = \frac{P \times R \times T}{100} \)
\( = \frac{1200 \times 12 \times 3}{100} = 12 \times 36 = \text{Rs } 432 \).
In simple words: Multiply 1200 by 12 and 3, then divide by 100 to get Rs 432.

Exam Tip: Cancel out the two zeroes in 1200 with the 100 in the denominator first.

Question 47. What rate gives Rs 280 as interest on a sum of Rs 56,000 in 2 years?
(a) 0.5%
(b) 0.25%
(c) 2.5%
(d) 0.05%
Answer: (b) 0.25%
\( R = \frac{I \times 100}{P \times T} \)
\( R = \frac{280 \times 100}{56000 \times 2} = \frac{28000}{112000} = \frac{28}{112} = \frac{1}{4}\% = 0.25\% \).
In simple words: Putting the values in the rate formula gives 1/4% or 0.25%.

Exam Tip: Notice that 28 divides into 112 exactly 4 times, giving 1/4 or 0.25%.

Question 48. Cost of an item is Rs 25. It was sold with a profit of 12%. What was the selling price?
(a) Rs 32
(b) Rs 28
(c) Rs 27
(d) Rs 30
Answer: (b) Rs 28
Profit = \( 12\% \text{ of } 25 = \frac{12}{100} \times 25 = \frac{12}{4} = \text{Rs } 3 \).
Selling Price = \( \text{CP} + \text{Profit} = 25 + 3 = \text{Rs } 28 \).
In simple words: A 12% profit on Rs 25 is Rs 3. Adding Rs 3 to Rs 25 gives Rs 28.

Exam Tip: Add profit to the cost price to calculate the final selling price.

Question 49. An item was sold for Rs 540, if the cost price of its item is Rs 600. What is the loss percentage?
(a) 12%
(b) 10%
(c) 15%
(d) 20%
Answer: (b) 10%
Loss = \( 600 - 540 = \text{Rs } 60 \).
Loss percentage = \( \frac{\text{Loss}}{\text{CP}} \times 100\% = \frac{60}{600} \times 100\% = 10\% \).
In simple words: The loss is Rs 60. Divide 60 by 600 and multiply by 100 to get 10%.

Exam Tip: Always use Cost Price (Rs 600) as the denominator for loss percentage.

Question 50. The cost of 13 books is Rs 299. What would be the cost of 3 books?
(a) Rs 46
(b) Rs 69
(c) Rs 92
(d) Rs 96
Answer: (b) Rs 69
Cost of 1 book = \( \frac{299}{13} = \text{Rs } 23 \).
Cost of 3 books = \( 3 \times 23 = \text{Rs } 69 \).
In simple words: One book costs Rs 23. Three books cost 3 times 23, which is Rs 69.

Exam Tip: Divide 299 by 13 carefully: 13 × 20 = 260, and 299 - 260 = 39, so 13 × 3 = 39, giving 23.

Question 51. Convert the following into fraction and Decimal
(i) \( 24\frac{1}{2}\% \)
(ii) 39.2%
Answer:
(i) For \( 24\frac{1}{2}\% \):
Fraction: \( \frac{49}{2}\% = \frac{49}{2 \times 100} = \frac{49}{200} \).
Decimal: \( \frac{49}{200} = \frac{49 \times 5}{1000} = \frac{245}{1000} = 0.245 \).
(ii) For 39.2%:
Fraction: \( \frac{39.2}{100} = \frac{392}{1000} = \frac{49}{125} \).
Decimal: \( \frac{39.2}{100} = 0.392 \).
In simple words: Divide the percent by 100 to get 49/200 and 0.245 for the first part, and 49/125 and 0.392 for the second part.

Exam Tip: Multiply numerator and denominator by 5 when the denominator is 200 to easily convert to decimals.

Question 52. Find the ratio of
(i) 1m to 1 Km.
(ii) 1 week of Feb. to Feb. month
Answer:
(i) Convert 1 km to metres: \( 1\text{ km} = 1000\text{ m} \).
Ratio = \( 1\text{ m} : 1000\text{ m} = 1:1000 \).
(ii) 1 week = 7 days. In an ordinary year, February has 28 days:
Ratio = \( 7\text{ days} : 28\text{ days} = 1:4 \).
(Note: In a leap year with 29 days, the ratio would be \( 7:29 \)).
In simple words: 1 km is 1000 m, giving a ratio of 1:1000. 1 week of 7 days compared to 28 days in February gives 1:4.

Exam Tip: Unless stated as a leap year, standard February has 28 days.

Question 53. If angles of a triangle are in the ratio 2:3:4. What is the value of greatest angle?
(a) 40°
(b) 60°
(c) 80°
(d) 50°
Answer: (c) 80°
Sum of angles of a triangle = 180°.
Total ratio parts = \( 2 + 3 + 4 = 9 \).
Greatest angle (4 parts) = \( \frac{4}{9} \times 180^\circ = 4 \times 20^\circ = 80^\circ \).
In simple words: The total is 9 parts for 180 degrees, so 1 part is 20 degrees. The biggest angle has 4 parts, which is 80 degrees.

Exam Tip: Use the angle sum property of a triangle (sum of angles = 180°) to find the value of one part.

Question 54. The cost of a flower vase is Rs 120. If the shopkeeper sells it at a loss of 10%, find the Selling price
(a) Rs 110
(b) Rs 108
(c) Rs 112
(d) Rs 132
Answer: (b) Rs 108
Loss = \( 10\% \text{ of } 120 = \frac{10}{100} \times 120 = \text{Rs } 12 \).
Selling Price = \( 120 - 12 = \text{Rs } 108 \).
In simple words: 10% of Rs 120 is Rs 12. Subtracting Rs 12 leaves Rs 108.

Exam Tip: Deduct the loss amount from the cost price to determine the selling price.

Question 55. Find the amount to be paid at the end of 3 yrs if the principal amount is Rs 1,200 at 10%p.a.
(a) Rs 1,300
(b) Rs 1,560
(c) Rs 1,498
(d) Rs 1360
Answer: (b) Rs 1,560
\( \text{Simple Interest} = \frac{P \times R \times T}{100} = \frac{1200 \times 10 \times 3}{100} = 12 \times 30 = \text{Rs } 360 \).
\( \text{Amount} = P + \text{SI} = 1200 + 360 = \text{Rs } 1560 \).
In simple words: The interest is Rs 360. Adding that to Rs 1200 gives a total of Rs 1,560.

Exam Tip: Amount = Principal + Simple Interest. Do not stop after calculating interest alone.

Question 56. Find the simple interest that Ram has to pay if he borrows Rs 500 for a period of 5 yrs at the rate of 5% p.a.
(a) Rs 200
(b) Rs 150
(c) Rs 100
(d) Rs 125
Answer: (d) Rs 125
\( \text{Simple Interest} = \frac{P \times R \times T}{100} = \frac{500 \times 5 \times 5}{100} = 5 \times 25 = \text{Rs } 125 \).
In simple words: Multiply 500 by 5 and 5, then divide by 100 to get Rs 125.

Exam Tip: Substitute directly into the simple interest formula: SI = (P × R × T) / 100.

Question 57. Selling price of a toy is Rs 540. If the profit made by the shopkeeper is 20%, find the cost price of the toy.
(a) Rs 500
(b) Rs 450
(c) Rs 520
(d) Rs 600
Answer: (b) Rs 450
\( \text{CP} = \frac{\text{SP} \times 100}{100 + \text{Profit}\%} \)
\( \text{CP} = \frac{540 \times 100}{120} = \frac{540 \times 5}{6} = 90 \times 5 = \text{Rs } 450 \).
In simple words: Rs 540 represents 120% of the cost price. Dividing 540 by 1.2 gives Rs 450.

Exam Tip: Check your answer: 20% of 450 is 90, and 450 + 90 = 540.

Question 58. Total numbers of beads in a bag are 20, if red beads are 8 and blue beads are 12, find out the percentage of each colour of beads.
Answer: Total beads = 20.
Percentage of red beads = \( \frac{8}{20} \times 100\% = 8 \times 5\% = 40\% \).
Percentage of blue beads = \( \frac{12}{20} \times 100\% = 12 \times 5\% = 60\% \).
Therefore, the bag contains 40% red beads and 60% blue beads.
In simple words: Red beads are 40% and blue beads are 60%. Together they add up to 100%.

Exam Tip: Make sure the sum of all individual percentages equals 100%.

Question 59. The cost of one packet of balls having 20 balls is Rs. 100, what will be the cost of such 24 balls.
Answer: Cost of 20 balls = Rs 100.
Cost of 1 ball = \( \frac{100}{20} = \text{Rs } 5 \).
Cost of 24 balls = \( 24 \times 5 = \text{Rs } 120 \).
Hence, the cost of 24 balls is Rs 120.
In simple words: Each ball costs Rs 5. So 24 balls cost 24 times 5, which is Rs 120.

Exam Tip: Divide to find the unit cost first, then multiply by the new quantity.

Question 60. Amina buys a book for Rs 275 and sells it at loss of 15%. How much does she sell it for?
(a) Rs 233.50
(b) Rs 233.75
(c) Rs 233.25
(d) Rs 240.00
Answer: (b) Rs 233.75
Loss = \( 15\% \text{ of } 275 = \frac{15}{100} \times 275 = \frac{4125}{100} = \text{Rs } 41.25 \).
Selling Price = \( 275 - 41.25 = \text{Rs } 233.75 \).
In simple words: The loss is Rs 41.25. Subtracting this from Rs 275 gives Rs 233.75.

Exam Tip: Be careful with decimals during subtraction: 275.00 - 41.25 = 233.75.

3 Mark Questions

Question 61. A man buys 3 oranges for Rs. 4 and sells 4 oranges for Rs. 6. Find his Gain or loss percent.
Answer: Cost Price of 3 oranges = Rs 4.
Cost Price of 1 orange = \( \text{Rs } \frac{4}{3} \).
Selling Price of 4 oranges = Rs 6.
Selling Price of 1 orange = \( \text{Rs } \frac{6}{4} = \text{Rs } \frac{3}{2} \).
Since \( \frac{3}{2} > \frac{4}{3} \) (1.50 > 1.33), there is a gain.
Gain = \( \frac{3}{2} - \frac{4}{3} = \frac{9 - 8}{6} = \text{Rs } \frac{1}{6} \).
Gain percentage = \( \frac{\text{Gain}}{\text{CP}} \times 100\% \)
\( = \frac{\frac{1}{6}}{\frac{4}{3}} \times 100\% = \left(\frac{1}{6} \times \frac{3}{4}\right) \times 100\% = \frac{1}{8} \times 100\% = 12.5\% \) (or \( 12\frac{1}{2}\% \)).
In simple words: Each orange is bought for Rs 4/3 and sold for Rs 3/2. The profit is 12.5%.

Exam Tip: Finding the cost and selling price of 1 orange (or an equal number like 12 oranges) makes comparison simple.

Question 62. A shopkeeper is selling an article of Rs.400, while he purchases it for Rs. 402. Find out loss percent of shopkeeper.
Answer: Cost Price (CP) = Rs 402.
Selling Price (SP) = Rs 400.
Since CP > SP, there is a loss.
Loss = \( 402 - 400 = \text{Rs } 2 \).
Loss percentage = \( \frac{\text{Loss}}{\text{CP}} \times 100\% \)
\( = \frac{2}{402} \times 100\% = \frac{1}{201} \times 100\% = \frac{100}{201}\% \approx 0.50\% \).
In simple words: The shopkeeper loses Rs 2 on Rs 402, which is about 0.50% loss.

Exam Tip: Keep the exact fraction 100/201% or round to two decimal places as 0.50%.

Question 63. One person divides his income in two parts if he gives 2 parts to Ram and 1 part to Shyam. What percentage of money he gives to Ram and Shyam separately.
Answer: Ratio of shares (Ram : Shyam) = 2 : 1.
Total parts = \( 2 + 1 = 3 \).
Percentage given to Ram = \( \frac{2}{3} \times 100\% = \frac{200}{3}\% = 66\frac{2}{3}\% \) (or \( 66.67\% \)).
Percentage given to Shyam = \( \frac{1}{3} \times 100\% = \frac{100}{3}\% = 33\frac{1}{3}\% \) (or \( 33.33\% \)).
In simple words: Ram gets two-thirds (66 2/3%) and Shyam gets one-third (33 1/3%) of the money.

Exam Tip: Verify that the two percentages add up to 100% (\( 66\frac{2}{3}\% + 33\frac{1}{3}\% = 100\% \)).

Question 64. Angles of a quadrilateral are in ratio 2 : 3 : 3 : 4, find out all the angles of quadrilateral.
Answer: Sum of all angles of a quadrilateral = 360°.
Total ratio parts = \( 2 + 3 + 3 + 4 = 12 \).
Value of 1 part = \( \frac{360^\circ}{12} = 30^\circ \).
First angle = \( 2 \times 30^\circ = 60^\circ \).
Second angle = \( 3 \times 30^\circ = 90^\circ \).
Third angle = \( 3 \times 30^\circ = 90^\circ \).
Fourth angle = \( 4 \times 30^\circ = 120^\circ \).
Therefore, the four angles are 60°, 90°, 90°, and 120°.
In simple words: Divide 360 degrees by 12 parts to get 30 degrees per part. The angles are 60, 90, 90, and 120 degrees.

Exam Tip: Confirm that the four angles sum to 360°: \( 60^\circ + 90^\circ + 90^\circ + 120^\circ = 360^\circ \).

Question 65. The loss in a company has decreased from 20 lacs to 5 lacs in one year. Find the loss decrease percentage.
Answer: Initial loss = 20 lacs.
New loss = 5 lacs.
Decrease in loss = \( 20 - 5 = 15\text{ lacs} \).
Loss decrease percentage = \( \frac{\text{Decrease}}{\text{Initial loss}} \times 100\% \)
\( = \frac{15}{20} \times 100\% = 15 \times 5\% = 75\% \).
Hence, the loss decreased by 75%.
In simple words: The loss dropped by 15 lacs out of 20 lacs, which is a 75% reduction.

Exam Tip: Divide by the original loss of 20 lacs, not by the new loss.

Question 66. Out of 30 students in a hostel, 8 are goingto market, 20 are going to watching T.V, rest of the students are studying. Convert all of them into percentage.
Answer: Total students = 30.
Students studying = \( 30 - (8 + 20) = 30 - 28 = 2 \).
1. Percentage going to market = \( \frac{8}{30} \times 100\% = \frac{80}{3}\% = 26\frac{2}{3}\% \) (or \( 26.67\% \)).
2. Percentage watching T.V = \( \frac{20}{30} \times 100\% = \frac{200}{3}\% = 66\frac{2}{3}\% \) (or \( 66.67\% \)).
3. Percentage studying = \( \frac{2}{30} \times 100\% = \frac{20}{3}\% = 6\frac{2}{3}\% \) (or \( 6.67\% \)).
In simple words: 26 2/3% are going to the market, 66 2/3% are watching TV, and 6 2/3% are studying.

Exam Tip: Calculate the remaining students who are studying first: 30 - (8 + 20) = 2.

5 Mark Questions

Question 67. Find the whole quantity if
(a) 12% of it is Rs 1080
(b) 40% of it is 500 km
Answer:
(a) Let the whole amount be \( x \):
\( 12\% \text{ of } x = 1080 \)
\( \frac{12}{100} \times x = 1080 \)

\( \implies x = \frac{1080 \times 100}{12} = 90 \times 100 = \text{Rs } 9000 \).
(b) Let the whole distance be \( y \):
\( 40\% \text{ of } y = 500\text{ km} \)
\( \frac{40}{100} \times y = 500 \)

\( \implies y = \frac{500 \times 100}{40} = \frac{500 \times 5}{2} = 250 \times 5 = 1250\text{ km} \).
In simple words: Divide the given number by its percentage and multiply by 100 to get Rs 9000 and 1250 km.

Exam Tip: Remember to include the correct units (Rs and km) in your final answers.

Question 68. Find the simple interest on Rs. 1200 from 2006 to 2009 at 6% per annum and also find the amount to be paid at the end of 3 years.
Answer: Principal (P) = Rs 1200.
Rate of interest (R) = 6% per annum.
Time (T) = \( 2009 - 2006 = 3\text{ years} \).
Simple Interest:
\( \text{SI} = \frac{P \times R \times T}{100} = \frac{1200 \times 6 \times 3}{100} = 12 \times 18 = \text{Rs } 216 \).
Total Amount to be paid:
\( \text{Amount} = P + \text{SI} = 1200 + 216 = \text{Rs } 1416 \).
In simple words: The interest for 3 years is Rs 216. Adding this to Rs 1200 gives a total of Rs 1416.

Exam Tip: Calculate the time in years by subtracting the starting year from the end year: 2009 - 2006 = 3 years.

Question 69. A man purchase two machines at Rs. 1200 each. On one he gain 20% and on the other he loses 20%. How much does he gain or lose in whole transaction.
Answer: Total Cost Price for both machines = \( 1200 + 1200 = \text{Rs } 2400 \).
For the first machine (20% gain):
Gain = \( 20\% \text{ of } 1200 = \frac{20}{100} \times 1200 = \text{Rs } 240 \).
Selling Price of first machine = \( 1200 + 240 = \text{Rs } 1440 \).
For the second machine (20% loss):
Loss = \( 20\% \text{ of } 1200 = \frac{20}{100} \times 1200 = \text{Rs } 240 \).
Selling Price of second machine = \( 1200 - 240 = \text{Rs } 960 \).
Total Selling Price = \( 1440 + 960 = \text{Rs } 2400 \).
Since Total SP = Total CP, there is neither gain nor loss in the whole transaction.
In simple words: He makes Rs 240 profit on the first machine and loses Rs 240 on the second. The profit and loss cancel each other out completely.

Exam Tip: When two items have the SAME cost price and equal gain and loss percentages, the overall transaction has zero gain and zero loss.

Question 70. A farmer borrowed Rs 5000 from a money lender at 9% per annum. After 4 years, he cleared the account by giving Rs 5500 and a cow to the money lender. Find the cost of the cow.
Answer: Principal (P) = Rs 5000.
Rate (R) = 9% per annum.
Time (T) = 4 years.
Calculate Simple Interest:
\( \text{SI} = \frac{5000 \times 9 \times 4}{100} = 50 \times 36 = \text{Rs } 1800 \).
Total amount due = \( P + \text{SI} = 5000 + 1800 = \text{Rs } 6800 \).
Amount settled by cash and cow:
\( 5500 + \text{Cost of cow} = 6800 \)

\( \implies \text{Cost of cow} = 6800 - 5500 = \text{Rs } 1300 \).
Therefore, the cost of the cow is Rs 1300.
In simple words: The total amount owed was Rs 6800. After paying Rs 5500 in cash, the cow made up the remaining Rs 1300.

Exam Tip: Find the total amount due first, then subtract the cash paid to get the value of the cow.

Question 71. Calculate the principle when
(i) Amount = Rs 4637.50 and simple interest = Rs 1137.50
(ii) Amount = Rs 10000 and simple interest = Rs 3750
(iii) Amount = Rs 7539 and simple interest = Rs 1523
(iv) What rates gives Rs 280 as interest on a sum of 56,000 in 2 years?
Answer:
Use the formula: \( \text{Principal} = \text{Amount} - \text{Simple Interest} \)
(i) \( \text{Principal} = 4637.50 - 1137.50 = \text{Rs } 3500 \).
(ii) \( \text{Principal} = 10000 - 3750 = \text{Rs } 6250 \).
(iii) \( \text{Principal} = 7539 - 1523 = \text{Rs } 6016 \).
(iv) Use the rate formula: \( R = \frac{I \times 100}{P \times T} \)
\( R = \frac{280 \times 100}{56000 \times 2} = \frac{28000}{112000} = 0.25\% \) (or \( \frac{1}{4}\% \)).
In simple words: Subtract interest from the total amount to find each principal. For the last part, use the rate formula to get 0.25%.

Exam Tip: Remember: Principal = Amount - Simple Interest. Keep decimal alignment correct while subtracting.

Question 72. 9900 students of Chennai appeared in the board examination. Out of them 35% secured 1st division, 45% secured 2nd division, 10% were allowed for compartmental examination and the rest failed. Find out the number of students in each category.
Answer: Total number of students = 9900.
1. Students with 1st division:
\( 35\% \text{ of } 9900 = \frac{35}{100} \times 9900 = 35 \times 99 = 3465 \text{ students} \).
2. Students with 2nd division:
\( 45\% \text{ of } 9900 = \frac{45}{100} \times 9900 = 45 \times 99 = 4455 \text{ students} \).
3. Students allowed for compartmental exam:
\( 10\% \text{ of } 9900 = \frac{10}{100} \times 9900 = 990 \text{ students} \).
4. Failed percentage = \( 100\% - (35\% + 45\% + 10\%) = 100\% - 90\% = 10\% \).
Number of students who failed:
\( 10\% \text{ of } 9900 = 990 \text{ students} \).
In simple words: 3465 students got 1st division, 4455 got 2nd division, 990 got compartment, and 990 failed.

Exam Tip: Verify your answer: 3465 + 4455 + 990 + 990 = 9900 students in total.

Question 73. An article was sold for Rs 250 with a profit of 5%. What was its cost price?
Answer: Selling Price (SP) = Rs 250.
Profit percentage = 5%.
Formula for Cost Price:
\( \text{CP} = \frac{\text{SP} \times 100}{100 + \text{Profit}\%} \)
\( \text{CP} = \frac{250 \times 100}{105} = \frac{25000}{105} \)
Divide numerator and denominator by 5:
\( \text{CP} = \frac{5000}{21} = \text{Rs } 238\frac{2}{21} \approx \text{Rs } 238.10 \).
Therefore, the cost price of the article was approximately Rs 238.10.
In simple words: Rs 250 is 105% of the cost price. Dividing 250 by 1.05 gives about Rs 238.10.

Exam Tip: Leave the final answer as a mixed fraction \( \text{Rs } 238\frac{2}{21} \) or round off to two decimal places as Rs 238.10.