CBSE Class 7 Mathematics Comparing Quantities Worksheet Set 01

Q.1. Find the ratio of 4 km to 400 m.
Answer: First, convert both quantities to the same unit.
1 km = 1000 m
4 km = \(4 \times 1000 = 4000\) m
Ratio = \(\frac{4000 \text{ m}}{400 \text{ m}} = \frac{10}{1}\)
Ratio = 10:1
In simple words: Convert kilometers into meters first so both numbers have the same unit, then simplify the fraction.
Exam Tip: Always check that units are identical before finding ratios.

Q.2. If six buckets cost Rs. 90, what would be the cost of 10 such buckets?
Answer: Cost of 6 buckets = Rs. 90
Cost of 1 bucket = \(\frac{90}{6} = \text{Rs. } 15\)
Cost of 10 buckets = \(15 \times 10 = \text{Rs. } 150\)
In simple words: Find the cost of a single item first by dividing, then multiply by the required number of items.

Exam Tip: Use the unitary method by finding the value of one unit first.

Q.3. Convert the following into percentage
a) 12/16 b) 0.05 c) 3.5
Answer: a) \(\frac{12}{16} = \frac{3}{4}\)
Percentage = \(\frac{3}{4} \times 100\% = 3 \times 25\% = 75\%\)
b) \(0.05 = \frac{5}{100}\)
Percentage = \(\frac{5}{100} \times 100\% = 5\%\)
c) \(3.5 = \frac{35}{10} = \frac{7}{2}\)
Percentage = \(\frac{7}{2} \times 100\% = 7 \times 50\% = 350\%\)
In simple words: Multiply any given number, fraction, or decimal by 100 to convert it into a percentage.

Exam Tip: Multiplying by 100% is equivalent to multiplying by 1, which does not change the value.

Q.4. A shop has 500 parts out of which 5 are defective. What percent are defective?
Answer: Total number of parts = 500
Number of defective parts = 5
Percentage of defective parts = \(\left(\frac{5}{500}\right) \times 100\%\)
\(= \frac{5}{5} \% = 1\%\)
In simple words: Put the defective parts over the total parts and multiply by 100.

Exam Tip: Percentage is always calculated with respect to the total quantity.

Q.5. If Ram’s salary is Rs. 50,000 per month, Ram spends 10% of his salary for helping the poor. Find how much salary he spends for helping the poor people? What value of Ram is depicted above?
Answer: Total salary = Rs. 50,000
Percentage spent on helping the poor = 10%
Amount spent = \(10\% \text{ of Rs. } 50,000\)
\(= \frac{10}{100} \times 50,000 = \text{Rs. } 5,000\)
Value depicted: Kindness, empathy, social responsibility, and helpfulness towards the needy.
In simple words: Calculate 10 percent of the total salary to find the exact money spent.

Exam Tip: Read word problems carefully to answer both the numerical part and the value-based question.

Q.6. If 8% children of a class of 25 like getting wet in rain how many children do not like getting wet in rain?
Answer: Total number of children = 25
Percentage of children who like getting wet = 8%
Percentage of children who do not like getting wet = \(100\% - 8\% = 92\%\)
Number of children who do not like getting wet = \(92\% \text{ of } 25\)
\(= \frac{92}{100} \times 25 = \frac{92}{4} = 23\)
In simple words: Find the percentage of children who dislike rain by subtracting from 100, then calculate that percentage of the class.

Exam Tip: You can also first find the number who like rain (\(8\% \text{ of } 25 = 2\)) and subtract from total (\(25 - 2 = 23\)).

Q.7. Find the whole quantity if
a) 25% of it is 9 b) 75% of it is 15
Answer: a) Let the whole quantity be \(x\).
\(25\% \text{ of } x = 9\)
\(\frac{25}{100} \times x = 9\)
\(x = 9 \times \frac{100}{25}\)
\(x = 9 \times 4 = 36\)
b) Let the whole quantity be \(y\).
\(75\% \text{ of } y = 15\)
\(\frac{75}{100} \times y = 15\)
\(y = 15 \times \frac{100}{75}\)
\(y = 15 \times \frac{4}{3} = 5 \times 4 = 20\)
In simple words: Set up an algebraic equation where a variable represents the unknown whole quantity, then solve for it.

Exam Tip: To find the whole quantity, multiply the given part by the reciprocal of the percentage fraction.

Q.8. If three angles of a triangle are in the ratio 2:3:4, find the value of each angle.
Answer: Let the angles be \(2x\), \(3x\), and \(4x\).
We know that the sum of angles in a triangle is \(180^\circ\).
\(2x + 3x + 4x = 180^\circ\)
\(9x = 180^\circ\)
\(x = \frac{180^\circ}{9} = 20^\circ\)
First angle = \(2x = 2 \times 20^\circ = 40^\circ\)
Second angle = \(3x = 3 \times 20^\circ = 60^\circ\)
Third angle = \(4x = 4 \times 20^\circ = 80^\circ\)
In simple words: Use variables with the given ratio, add them up to equal 180 degrees, solve for the variable, and substitute back.

Exam Tip: Always verify your answer by checking if the sum of the calculated angles equals 180 degrees.

Q.9. If the marks of Rohit in a test increased from 20 to 30, find the percentage increase.
Answer: Original value = 20
New value = 30
Increase in marks = \(30 - 20 = 10\)
Percentage increase = \(\left(\frac{\text{Increase}}{\text{Original Value}}\right) \times 100\%\)
\(= \left(\frac{10}{20}\right) \times 100\%\)
\(= \frac{1}{2} \times 100\% = 50\%\)
In simple words: Divide the amount of increase by the starting number, then multiply by 100.

Exam Tip: The base for percentage increase or decrease is always the original initial value.

Q.10. If the price of a shirt decreased from Rs.80 to Rs.60, find the percentage decrease.
Answer: Original price = Rs. 80
New price = Rs. 60
Decrease in price = \(80 - 60 = \text{Rs. } 20\)
Percentage decrease = \(\left(\frac{\text{Decrease}}{\text{Original Price}}\right) \times 100\%\)
\(= \left(\frac{20}{80}\right) \times 100\%\)
\(= \frac{1}{4} \times 100\% = 25\%\)
In simple words: Find the drop in price, divide by the initial price, and multiply by 100.

Exam Tip: Keep the original value in the denominator, never the new reduced value.

Q.11. Cost of an item is Rs.50, it was sold with the profit of 12%, find the selling price of the item.
Answer: Cost Price (CP) = Rs. 50
Profit percent = 12%
Profit amount = \(12\% \text{ of } 50\)
\(= \frac{12}{100} \times 50 = \text{Rs. } 6\)
Selling Price (SP) = \(\text{Cost Price} + \text{Profit}\)
\(\text{SP} = 50 + 6 = \text{Rs. } 56\)
In simple words: Calculate the profit amount from the cost price and add it to the cost price to get the selling price.

Q.12. A shopkeeper bought a table for Rs. 375 and sold it for Rs. 400, find his gain or loss percent.
Answer: Cost Price (CP) = Rs. 375
Selling Price (SP) = Rs. 400
Since \(\text{SP} > \text{CP}\), there is a gain.
Gain = \(\text{SP} - \text{CP} = 400 - 375 = \text{Rs. } 25\)
Gain percent = \(\left(\frac{\text{Gain}}{\text{CP}}\right) \times 100\%\)
\(= \left(\frac{25}{375}\right) \times 100\%\)
\(= \left(\frac{1}{15}\right) \times 100\% = \frac{100}{15}\% = \frac{20}{3}\% = 6.67\%\)
In simple words: Subtract cost price from selling price to find profit, then find what percentage of the cost price that profit is.

Exam Tip: Profit or loss percent is always calculated on the Cost Price.

Q.13. An item was sold for Rs.540 at a loss off 5%, what was its cost price?
Answer: Selling Price (SP) = Rs. 540
Loss percent = 5%
Let the Cost Price (CP) be \(x\).
Loss = \(5\% \text{ of } x = \frac{5}{100}x\)
\(\text{SP} = \text{CP} - \text{Loss}\)
\(540 = x - \frac{5}{100}x\)
\(540 = \frac{95}{100}x\)
\(x = 540 \times \frac{100}{95}\)
\(x = 540 \times \frac{20}{19} = \frac{10800}{19} = \text{Rs. } 568.42\)
In simple words: Set up an equation where selling price equals cost price minus the loss percentage, and solve for cost price.

Exam Tip: Formula for Cost Price when SP and loss percent are given: \(\text{CP} = \frac{\text{SP} \times 100}{100 - \text{Loss}\%}\).

Q.14. If Rita borrowed Rs.6050 at 6.5% rate of interest per annum, find the simple interest and the amount to be paid at the end of 3 years.
Answer: Principal (\(P\)) = Rs. 6050
Rate (\(R\)) = 6.5% per annum
Time (\(T\)) = 3 years
Simple Interest (\(SI\)) = \(\frac{P \times R \times T}{100}\)
\(SI = \frac{6050 \times 6.5 \times 3}{100}\)
\(SI = \frac{6050 \times 19.5}{100} = \frac{117975}{100} = \text{Rs. } 1179.75\)
Amount (\(A\)) = \(P + SI\)
\(A = 6050 + 1179.75 = \text{Rs. } 7229.75\)
In simple words: Multiply Principal, Rate, and Time then divide by 100 to find interest. Add interest to principal to get total amount.

Exam Tip: Always remember to add the Simple Interest back to the Principal to find the final total Amount.

Q.15. If you have Rs. 2400 in your account and the interest rate is 5% after hwo many years would you earn Rs.240 as interest?
Answer: Principal (\(P\)) = Rs. 2400
Rate (\(R\)) = 5% per annum
Simple Interest (\(SI\)) = Rs. 240
Time (\(T\)) = ?
\(SI = \frac{P \times R \times T}{100}\)
\(240 = \frac{2400 \times 5 \times T}{100}\)
\(240 = 24 \times 5 \times T\)
\(240 = 120 \times T\)
\(T = \frac{240}{120} = 2 \text{ years}\)
In simple words: Substitute the known values into the simple interest formula and solve for time.

Q.16. On a certain sum the simple interest paid after 3 years is Rs. 450 at 5% rate of interest per annum. Find the sum.
Answer: Simple Interest (\(SI\)) = Rs. 450
Time (\(T\)) = 3 years
Rate (\(R\)) = 5% per annum
Principal (\(P\)) = ?
\(SI = \frac{P \times R \times T}{100}\)
\(450 = \frac{P \times 5 \times 3}{100}\)
\(450 = \frac{15P}{100}\)
\(15P = 45000\)
\(P = \frac{45000}{15} = \text{Rs. } 3000\)
In simple words: Use the simple interest formula with the given interest, rate, and time to find the missing principal sum.

Exam Tip: Formula for principal: \(P = \frac{SI \times 100}{R \times T}\).

Question. Find the ratio in the simplest form :
(i) 3 kg to 12 kg
(ii) 80 paise to Rs. 2
(iii) 12.8 m to 3.2 m.
Answer : (i) 1 : 4 (ii) 2 : 5 (iii) 4 : 1

Question. Amit’s salary is Rs. 42000 p.m. and he pays Rs. 6000 as income tax every month. Find the ratio of his income to the income tax.
Answer : 7 : 1

Question. 6 kg. of rice is enough for 20 people. How much rice is required for 100 people?
Answer : 30 kg

Question. At what rate percent per annum will Rs. 800 amount to Rs. 1000 in one year?
Answer : 25%

Question. The length of a ribbon is 10 m and its width is 25 cm. Find the ratio of width to the length.
Answer : 1 : 40

Question. A school has 800 students. There are 500 girls and remaining are boys. Find the ratio of boys and girls
Answer : 3 : 5

Question. Find the cost of 10 pencils, if cost of 6 pencils is Rs. 72.
Answer : Rs. 120

Question. Convert the following percentage into decimals :
(a) 10.2%
(b) 40%
(c) 0.07%
Answer : (a) = 0.102% (b) = 0.40 (c) 0.0007

Question. Express the following ratios into the simplest form :
(a) 15 : 18
(b) 32 : 40
(c) 108 : 12
Answer : (a) 5 : 6 (b) 4 : 5 (c) 9 : 1

Question. Find equivalent ratio for each of the following :
(a) 2 : 5
(b) 4 : 9
Answer : (a) 4 : 10 (b) 8 : 18

Question. The first three terms of a proportion are 2, 3, and 6. Find the fourth term.
Answer : 9

Question. Which ratio is greater :
(i) 15 : 18 or 24 : 27?
(ii) 15 : 27 or 32 : 40?
Answer : (i) 24 : 27 (ii) 32 : 40

Question. Bananas are available in the market at the rate of Rs. 24 per dozen. Find the cost of 10 bananas.
Answer : Rs. 20

Question. Find :
(a) 50% of 175
(b) 75% of Rs. 120
(c) 25% of 64 kg.
Answer : (a) 87.5 (b) Rs. 90 (c) 16 kg.

Question. The cost price of 4 articles is the same as the selling price of 3 articles. Find the profit percent.
Answer : 33(1/3)%

Question. Convert the following fractions into percent :
(a) 12/16
(b) 49/60
(c) 44
Answer : (a) = 75% (b) = 98% (c) = 100%

Question. What percent of 4 km is 160 gm.
Answer : 4%

Question. Shyam Lal sold a horse for Rs. 1560 and gained 4%. Find the cost price.
Answer : Rs. 1500

Question. If 75 percent of students in a class like to play hockey, what percentage of students do not like to play hockey?
Answer : 25%

Question. Find the simple interest on Rs. 400 for 3(1/3) years at 3% p.a.
Answer : Rs. 40

Question. 75% of x = 15. Find x.
Answer : x = 20

Question. Ram saves Rs. 500 from his salary. If this is 25% of his salary, what is his salary?
Answer : Rs. 2000

Question. A man sold a watch at Rs. 3,800 and lost 5%. What was the cost price?
Answer : Rs. 4000

Question. Ram purchased a radio set for Rs. 400 and sold it to Shyam at a profit of 25%. Shyam sold it to Mohan at a loss of 10%. For how much money did Mohan buy it?
Answer : Rs. 450

Question. Express the following as percent :
(a) 3:15
(b) 4 : 5
(c) 15 : 40
Answer : (a) = 20% (b) = 80% (c) = 37½%