CBSE Class 7 Mathematics Comparing Quantities Worksheet Set 05

Multiple Choice Questions

Question 1. Ratio of Rs.75 to Rs200 is
(a) 75:2
(b) 3:8
(c) 75:20
(d) 75:200
Answer: (b) 3:8
Express both quantities in ratio form as a fraction:
\( \frac{75}{200} \)
Divide the top and bottom terms by 25:
\( \frac{75 \div 25}{200 \div 25} = \frac{3}{8} \)
Therefore, the simplified ratio is \( 3:8 \).
In simple words: Divide both numbers by 25. This simplifies the fraction to 3 over 8, giving the ratio 3:8.

Exam Tip: Verify that both terms share identical units before reducing. In this problem, both values are already stated in rupees.

Question 2. The simplest form of 57:133 is
(a) 1:3
(b) 3:7
(c) 2:5
(d) 4:6
Answer: (b) 3:7
Write the given terms in fractional form:
\( \frac{57}{133} \)
Both 57 and 133 share a common factor of 19:
\( \frac{57 \div 19}{133 \div 19} = \frac{3}{7} \)
Hence, the ratio in lowest terms is \( 3:7 \).
In simple words: Divide 57 and 133 by 19. That leaves 3 and 7, so the simplest ratio is 3:7.

Exam Tip: Practice tables of prime numbers like 13, 17, and 19 to spot common factors quickly during tests.

Question 3. 50 g is what percent of 2 kg
(a) 25%
(b) 20%
(c) 2.5%
(d) 50%
Answer: (c) 2.5%
Change the larger unit from kilograms into grams:
\( 2\text{ kg} = 2 \times 1000\text{ g} = 2000\text{ g} \)
Now set up the percentage calculation:
\( \text{Percentage} = \frac{50}{2000} \times 100\% \)
\( = \frac{50}{20}\% = 2.5\% \).
In simple words: Turn 2 kg into 2000 g first. Then divide 50 by 2000 and multiply by 100 to get 2.5%.

Exam Tip: Never compute ratios or percentages using different units. Convert to the smaller unit first.

Question 4. If S.P=510, CP=450 what will be gain
(a) 960
(b) 60
(c) 100
(d) None
Answer: (b) 60
Since selling price exceeds cost price, a gain is earned.
Apply the gain formula:
\( \text{Gain} = \text{S.P.} - \text{C.P.} \)
\( \text{Gain} = 510 - 450 = 60 \).
In simple words: Take away the cost price of 450 from the selling price of 510 to find the profit of 60.

Exam Tip: Remember that Gain = S.P. - C.P. Do not mix up the total gain value with the gain percentage.

Question 5. 150% of 50 is
(a) 75
(b) 150
(c) 100
(d) 300
Answer: (a) 75
Convert the percentage into a fraction and multiply:
\( \frac{150}{100} \times 50 \)
Simplify by cancelling common factors:
\( \frac{150}{2} = 75 \).
In simple words: Multiply 150 by 50 and divide by 100. The result is 75.

Exam Tip: Cancel out zeroes between 50 and 100 before multiplying to make mental math much faster.

Question 6. Find the value of x if
(a) 10% of x is 27
(b) 1% of x is 8
(c) 45% of x is 180
Answer:
(a) Given \( 10\% \text{ of } x = 27 \):
\( \frac{10}{100} \times x = 27 \)

\( \implies x = \frac{27 \times 100}{10} = 270 \)
(b) Given \( 1\% \text{ of } x = 8 \):
\( \frac{1}{100} \times x = 8 \)

\( \implies x = 8 \times 100 = 800 \)
(c) Given \( 45\% \text{ of } x = 180 \):
\( \frac{45}{100} \times x = 180 \)

\( \implies x = \frac{180 \times 100}{45} = 4 \times 100 = 400 \)
In simple words: Change each percentage to a fraction over 100. Then multiply across to solve for x.

Exam Tip: When isolating x, multiply both sides by 100 and divide by the given percentage rate.

Question 7. The length of a room is 5.6 m and its breadth is 4.2 m .Find the ratio of its
(a) length to breadth
(b) breadth to length
Answer:
(a) Ratio of length to breadth:
\( \frac{\text{Length}}{\text{Breadth}} = \frac{5.6}{4.2} = \frac{56}{42} \)
Divide both terms by 14:
\( \frac{56 \div 14}{42 \div 14} = \frac{4}{3} \)
The ratio is \( 4:3 \).
(b) Ratio of breadth to length:
\( \frac{\text{Breadth}}{\text{Length}} = \frac{4.2}{5.6} = \frac{42}{56} \)
Divide both terms by 14:
\( \frac{42 \div 14}{56 \div 14} = \frac{3}{4} \)
The ratio is \( 3:4 \).
In simple words: Clear the decimals by multiplying by 10 to get 56 and 42. Dividing both by 14 gives 4:3 for length to breadth and 3:4 for breadth to length.

Exam Tip: The order of quantities matters in ratios. Length to breadth is 4:3, while breadth to length is its inverse, 3:4.

Question 8. Convert the following in to percent
(a) 12/16
(b) 49/50
(c) 4/4
Answer:
(a) Multiply the fraction by 100%:
\( \frac{12}{16} \times 100\% = \frac{3}{4} \times 100\% = 75\% \)
(b) Multiply the fraction by 100%:
\( \frac{49}{50} \times 100\% = 49 \times 2\% = 98\% \)
(c) Multiply the fraction by 100%:
\( \frac{4}{4} \times 100\% = 1 \times 100\% = 100\% \)
In simple words: Multiply each fraction by 100 and write a percent sign at the end.

Exam Tip: Simplify the fraction first whenever possible to make multiplication with 100 straightforward.

Question 10. Convert the following percentage in to decimals
(a) 10.2%
(b) 40%
(c) 0.07%
(d) 12 1/5 %
Answer:
(a) Divide the percentage value by 100:
\( \frac{10.2}{100} = 0.102 \)
(b) Divide the percentage value by 100:
\( \frac{40}{100} = 0.4 \)
(c) Divide the percentage value by 100:
\( \frac{0.07}{100} = 0.0007 \)
(d) Convert the mixed fraction into a decimal percentage first:
\( 12\frac{1}{5}\% = 12.2\% \)
Now divide by 100:
\( \frac{12.2}{100} = 0.122 \)
In simple words: Remove the percent symbol and slide the decimal point two spots to the left.

Exam Tip: When moving decimals on very small values like 0.07%, remember to add placeholder zeroes carefully.

Question 11. There are 25 radios, 16 of them are out of order. What percent of radios are out of order?
Answer: Total number of radios = 25.
Number of non-working radios = 16.
Find the percentage:
\( \text{Percentage out of order} = \frac{16}{25} \times 100\% \)
\( = 16 \times 4\% = 64\% \).
Therefore, 64% of the radios are out of order.
In simple words: Divide 16 faulty radios by 25 total radios and multiply by 100 to get 64%.

Exam Tip: Since 25 goes into 100 exactly 4 times, simply multiply the numerator by 4 to get the percent directly.

Question 12. The selling price of an item is Rs. 8000. It is sold at a loss of 10%. Find the cost price.
Answer: Selling price (S.P.) = Rs. 8000.
Loss percentage = 10%.
Use the formula linking selling price and cost price:
\( \text{S.P.} = \text{C.P.} \times \left(1 - \frac{\text{Loss}\%}{100}\right) \)
\( 8000 = \text{C.P.} \times \left(1 - \frac{10}{100}\right) \)
\( 8000 = \text{C.P.} \times \frac{90}{100} \)

\( \implies \text{C.P.} = \frac{8000 \times 100}{90} \)

\( \implies \text{C.P.} = \frac{80000}{9} \approx \text{Rs. } 8888.89 \)
Thus, the cost price of the item is Rs. 8888.89.
In simple words: A 10% loss means Rs. 8000 is 90% of the cost price. Dividing 8000 by 0.9 gives Rs. 8888.89.

Exam Tip: Always remember that loss percentage is calculated on cost price, never on selling price.

Question 14. Out of 25000 voters in a constituency, 72% voted. Find the percentage of voters who did not vote.Can you find how many actually did not vote?
Answer: Total number of voters = 25,000.
Percentage of citizens who voted = 72%.
Percentage of citizens who did not vote:
\( 100\% - 72\% = 28\% \).
Number of citizens who did not vote:
\( 28\% \text{ of } 25000 = \frac{28}{100} \times 25000 \)
\( = 28 \times 250 = 7000 \).
Hence, 28% of the voters did not vote, which represents 7,000 voters.
In simple words: Subtract 72% from 100% to get 28%. Then take 28% of 25,000 to find that 7,000 people stayed away from voting.

Exam Tip: Answer both questions explicitly: first state the non-voting percentage, then provide the head count.

Question 15. The population of a city decreased from 25,000 to 24,500.Find the percentage decreased?
Answer: Initial population = 25,000.
Final population = 24,500.
Calculate the population decline:
\( \text{Decrease} = 25000 - 24500 = 500 \).
Now calculate the percentage decrease based on the original population:
\( \text{Percentage decrease} = \frac{\text{Decrease}}{\text{Original Population}} \times 100\% \)
\( = \frac{500}{25000} \times 100\% = 2\% \).
Thus, the city population dropped by 2%.
In simple words: The population went down by 500 people. Divide 500 by the starting 25,000 and multiply by 100 to get a 2% drop.

Exam Tip: Always place the initial (original) population in the denominator when calculating percentage decrease.

Question 16. Find the Simple Interest and Amount when
(a) Principal= Rs.600 rate=5% p.a time=3 years
(b) Principal= Rs.900 rate=6 %p.a time=6 months.
(c) Principal= Rs.1200 rate=10% p.a time= 5 years.
Answer:
Use the standard formulas:
\( \text{Simple Interest (S.I.)} = \frac{P \times R \times T}{100} \)
\( \text{Amount} = P + \text{S.I.} \)
(a) Given \( P = \text{Rs. } 600 \), \( R = 5\% \), and \( T = 3\text{ years} \):
\( \text{S.I.} = \frac{600 \times 5 \times 3}{100} = 6 \times 15 = \text{Rs. } 90 \)
\( \text{Amount} = 600 + 90 = \text{Rs. } 690 \)
(b) Given \( P = \text{Rs. } 900 \), \( R = 6\% \), and \( T = 6\text{ months} = \frac{6}{12}\text{ year} = 0.5\text{ year} \):
\( \text{S.I.} = \frac{900 \times 6 \times 0.5}{100} = 9 \times 3 = \text{Rs. } 27 \)
\( \text{Amount} = 900 + 27 = \text{Rs. } 927 \)
(c) Given \( P = \text{Rs. } 1200 \), \( R = 10\% \), and \( T = 5\text{ years} \):
\( \text{S.I.} = \frac{1200 \times 10 \times 5}{100} = 12 \times 50 = \text{Rs. } 600 \)
\( \text{Amount} = 1200 + 600 = \text{Rs. } 1800 \)
In simple words: Multiply principal, rate, and time in years, then divide by 100 for interest. Add interest to principal for the final amount.

Exam Tip: In part (b), convert months into years by dividing by 12 before calculating simple interest.

Question 17. Tushar borrowed Rs.550 at 15% per annum from a friend for 2 years. Calculate the interest paid and amount paid by Tushar?
Answer: Principal (\( P \)) = Rs. 550.
Rate (\( R \)) = 15% per annum.
Time (\( T \)) = 2 years.
Calculate the interest:
\( \text{Interest} = \frac{P \times R \times T}{100} = \frac{550 \times 15 \times 2}{100} \)
\( = \frac{550 \times 30}{100} = 55 \times 3 = \text{Rs. } 165 \).
Calculate the total repayment amount:
\( \text{Amount} = \text{Principal} + \text{Interest} \)
\( = 550 + 165 = \text{Rs. } 715 \).
Tushar paid Rs. 165 in interest and returned Rs. 715 in total.
In simple words: The interest is Rs. 165. Adding this to the borrowed sum gives a total repayment of Rs. 715.

Exam Tip: Make sure to clearly present both values - interest and total amount - to get full marks.

Question 18. Mohit bought a cycle for Rs.1850. He sold it at a profit of 8%. Find the selling price of the cycle.
Answer: Cost price (C.P.) = Rs. 1850.
Profit percentage = 8%.
Find the profit value:
\( \text{Profit} = \frac{8}{100} \times 1850 = 8 \times 18.5 = \text{Rs. } 148 \).
Find the selling price:
\( \text{S.P.} = \text{C.P.} + \text{Profit} \)
\( = 1850 + 148 = \text{Rs. } 1998 \).
Therefore, the selling price of the cycle is Rs. 1998.
In simple words: Work out 8% of 1850, which is 148. Add that to the cost price to get Rs. 1998.

Exam Tip: You can also find the selling price directly by calculating 108% of the cost price.

Question 19. Karim bought a motorcycle for Rs 13100 .After 6 months he sold at loss of 12%.Find the selling price of the motorcycle.
Answer: Cost price (C.P.) = Rs. 13100.
Loss percentage = 12%.
Calculate the loss amount:
\( \text{Loss} = \frac{12}{100} \times 13100 = 12 \times 131 = \text{Rs. } 1572 \).
Calculate the selling price:
\( \text{S.P.} = \text{C.P.} - \text{Loss} \)
\( = 13100 - 1572 = \text{Rs. } 11528 \).
Therefore, Karim sold the motorcycle for Rs. 11528.
In simple words: 12% of 13100 is 1572. Subtracting 1572 from 13100 gives the selling price of Rs. 11528.

Exam Tip: The 6-month timeframe is extra information here because the loss is given directly as 12% of the purchase price.

Question 20. Prithvi bought a Motorbike for Rs.98,000. He had to sell it for Rs.83,500. Find his profit or loss percentage?
Answer: Cost price (C.P.) = Rs. 98,000.
Selling price (S.P.) = Rs. 83,500.
Since S.P. is less than C.P., this transaction resulted in a loss.
\( \text{Loss} = \text{C.P.} - \text{S.P.} = 98000 - 83500 = \text{Rs. } 14500 \).
Calculate loss percentage:
\( \text{Loss}\% = \frac{\text{Loss}}{\text{C.P.}} \times 100\% \)
\( = \frac{14500}{98000} \times 100\% \)
\( = \frac{1450}{98}\% = \frac{725}{49}\% \approx 14.8\% \).
Thus, Prithvi suffered a loss of approximately 14.8% (or \( 14\frac{39}{49}\% \)).
In simple words: The bike was sold at a loss of Rs. 14,500. Dividing 14,500 by 98,000 gives a loss of roughly 14.8%.

Exam Tip: Always state clearly whether the transaction was a profit or a loss before writing down the percentage.

Question 21. By selling a sofa set for Rs.14,400 a shopkeeper gains 20%.Find the cost price of the sofa set?
Answer: Selling price (S.P.) = Rs. 14,400.
Gain percentage = 20%.
Use the relationship between selling price and cost price:
\( \text{S.P.} = \text{C.P.} \times \left(1 + \frac{\text{Gain}\%}{100}\right) \)
\( 14400 = \text{C.P.} \times \left(1 + \frac{20}{100}\right) \)
\( 14400 = \text{C.P.} \times \frac{120}{100} = \text{C.P.} \times \frac{6}{5} \)

\( \implies \text{C.P.} = \frac{14400 \times 5}{6} = 2400 \times 5 = \text{Rs. } 12000 \).
Hence, the cost price of the sofa set is Rs. 12,000.
In simple words: The selling price is 120% of the cost price. Dividing 14,400 by 1.2 gives the original cost of Rs. 12,000.

Exam Tip: Do not find 20% of Rs. 14,400 and subtract it. Gain percentage is always computed on the cost price.

Question 22. Karan and shashank borrowed Rs. 6,000 each at the rate of 12% per annum for a period of 2 years and 3 years respectively. Find the difference between the interest paid by them?.
Answer: Both borrowed a principal of Rs. 6000 at 12% per annum.
Interest paid by Karan over 2 years:
\( \text{Interest}_{\text{Karan}} = \frac{6000 \times 12 \times 2}{100} = 60 \times 24 = \text{Rs. } 1440 \).
Interest paid by Shashank over 3 years:
\( \text{Interest}_{\text{Shashank}} = \frac{6000 \times 12 \times 3}{100} = 60 \times 36 = \text{Rs. } 2160 \).
Difference in interest paid:
\( 2160 - 1440 = \text{Rs. } 720 \).
Alternatively, since their loan periods differ by \( 3 - 2 = 1\text{ year} \):
\( \text{Difference} = \frac{6000 \times 12 \times 1}{100} = \text{Rs. } 720 \).
Therefore, the difference between the interest paid is Rs. 720.
In simple words: Shashank held the money for 1 year longer, so the difference is simply 1 year of interest on Rs. 6,000, which is Rs. 720.

Exam Tip: Using the difference in time (1 year) allows you to find the difference in interest directly in one step.

Question 23. What rate gives Rs.280 as interest on a sum of Rs.56,000 in 2 years?
Answer: Simple Interest (\( \text{S.I.} \)) = Rs. 280.
Principal (\( P \)) = Rs. 56,000.
Time (\( T \)) = 2 years.
Apply the formula for rate of interest:
\( R = \frac{\text{S.I.} \times 100}{P \times T} \)
\( R = \frac{280 \times 100}{56000 \times 2} \)
\( R = \frac{28000}{112000} = \frac{28}{112} = \frac{1}{4}\% = 0.25\% \).
Thus, the required annual rate of interest is 0.25% (or \( \frac{1}{4}\% \)).
In simple words: Substitute the given numbers into the rate formula. Simplifying gives an annual rate of 0.25%.

Exam Tip: Take care when simplifying: 28 goes into 112 exactly 4 times, giving 1/4%, which equals 0.25%.

Question 24. Selling price of a toy car is Rs. 540.If the profit made by the shopkeeper is 20%.What is the cost price of this toy?
Answer: Selling price (S.P.) = Rs. 540.
Profit percentage = 20%.
Use the formula connecting selling price and cost price:
\( \text{S.P.} = \text{C.P.} \times \left(1 + \frac{\text{Profit}\%}{100}\right) \)
\( 540 = \text{C.P.} \times \left(1 + \frac{20}{100}\right) \)
\( 540 = \text{C.P.} \times \frac{120}{100} = \text{C.P.} \times \frac{6}{5} \)

\( \implies \text{C.P.} = \frac{540 \times 5}{6} = 90 \times 5 = \text{Rs. } 450 \).
Thus, the cost price of the toy car is Rs. 450.
In simple words: The selling price represents 120% of the cost price. Dividing 540 by 1.2 gives the original price of Rs. 450.

Exam Tip: Verify your answer by adding 20% of 450 (which is 90) back to 450 to confirm it equals 540.