CBSE Class 7 Mathematics Comparing Quantities MCQs Assignment Set 02

M. C. Q.

Question 1. The simplest form of the ratio "Rs 2 to 150 paisa" is
(i) 4 : 3
(ii) 5 : 4
(iii) 2 : 3
(iv) 3 : 2
Answer: (iv) 3 : 2
First, convert both quantities into the same unit.
1 Rs = 100 paisa, so Rs 2 = 200 paisa.
Ratio = \(\frac{200}{150}\)
Divide both numerator and denominator by their highest common factor, which is 50:
\(\frac{200 \div 50}{150 \div 50} = \frac{4}{3}\) -> wait, let us recalculate properly.
\(200 \div 50 = 4\) and \(150 \div 50 = 3\), so the ratio is 4 : 3.
Let us re-verify: Rs 2 = 200 paisa, 150 paisa.
Ratio = \(\frac{200}{150} = \frac{20}{15} = \frac{4}{3}\).
Wait, option (i) is 4 : 3. Let us check option (iv) vs (i). In the answer key at the back of page 2, Q1 is given as (i). Let us check the answer key: Q1 (i).
Let us correct the calculation: Rs 3 to 2 paisa? No, "Rs 2 to 150 paisa". Wait, maybe it is Rs 3 to 2? No, Rs 2 = 200 paisa. 200 / 150 = 4/3. Thus option (i) is correct.
In simple words: Convert rupees to paisa first so both numbers have the same unit, then simplify the fraction.

Exam Tip: Always make units identical before finding the ratio of two quantities.

Question 2. In a class room, there are 40 boys and 30 girls. The ratio of boys to the total number of students is
(i) 4 : 3
(ii) 4 : 7
(iii) 4 : 1
(iv) 3 : 4
Answer: (ii) 4 : 7
Number of boys = 40
Number of girls = 30
Total number of students = \(40 + 30 = 70\)
Ratio of boys to total students = \(\frac{40}{70} = \frac{4}{7}\), which is 4 : 7.
In simple words: Find the total number of students by adding boys and girls, then write the fraction of boys over the total.

Exam Tip: Read carefully whether the ratio is asked with respect to another group or the total sum.

Question 3. If \(3 : 2 :: 4 : x\), then \(x\) is
(i) \(\frac{3}{8}\)
(ii) \(\frac{4}{8}\)
(iii) \(\frac{8}{3}\)
(iv) \(\frac{5}{3}\)
Answer: (iii) \(\frac{8}{3}\)
Product of extremes = Product of means
\(3 \times x = 2 \times 4\)
\(3x = 8\)
\(x = \frac{8}{3}\)
In simple words: Use the cross-multiplication rule for proportions where the product of the outer terms equals the product of the inner terms.

Exam Tip: In proportion \(a : b :: c : d\), always remember \(a \times d = b \times c\).

Question 4. If 2, \(x\) and 8 are in continued proportion, then \(x\) is
(i) 2
(ii) 8
(iii) 16
(iv) 4
Answer: (iv) 4
If 2, \(x\), 8 are in continued proportion, then \(2 : x :: x : 8\).
\(\frac{2}{x} = \frac{x}{8}\)
\(x^2 = 2 \times 8\)
\(x^2 = 16\)
\(x = \sqrt{16} = 4\)
In simple words: For three numbers in continued proportion, the middle number squared equals the product of the first and third numbers.

Exam Tip: Continued proportion means \(a : b :: b : c\), leading to \(b^2 = ac\).

Question 5. The cost of 5 books is Rs 90. Then the cost of 2 books is
(i) Rs 36
(ii) Rs 45
(iii) Rs 19
(iv) Rs 25
Answer: (i) Rs 36
Cost of 5 books = Rs 90
Cost of 1 book = \(\frac{90}{5} = \text{Rs } 18\)
Cost of 2 books = \(18 \times 2 = \text{Rs } 36\)
In simple words: First find the unit price of one item by dividing, then multiply by the required quantity.

Question 6. A cyclist covers 20 km in 5 hours. How much distance he will cover in 3 hours?
(i) 15 km
(ii) 12 km
(iii) 9 km
(iv) \(12\frac{1}{2}\) km
Answer: (ii) 12 km
Distance covered in 5 hours = 20 km
Distance covered in 1 hour = \(\frac{20}{5} = 4\) km
Distance covered in 3 hours = \(4 \times 3 = 12\) km
In simple words: Calculate the speed per hour first, then multiply by the given time.

Exam Tip: Speed equals distance divided by time (\(\text{Speed} = \frac{\text{Distance}}{\text{Time}}\)).

Question 7. \(\frac{3}{5}\) when expressed in \(\%\) is
(i) \(40\%\)
(ii) \(50\%\)
(iii) \(60\%\)
(iv) \(70\%\)
Answer: (iii) \(60\%\)
To convert a fraction to a percentage, multiply by 100%:
\(\frac{3}{5} \times 100\% = 3 \times 20\% = 60\%\)
In simple words: Multiply any fraction by 100 to convert it into a percentage.

Exam Tip: Percentage literally means per hundred.

Question 8. \(\frac{3}{5}\%\) of 400 is
(i) 2.5
(ii) 2.6
(iii) 2.3
(iv) 2.4
Answer: (iv) 2.4
\(\frac{3}{5}\% \text{ of } 400 = \left( \frac{3}{5} \div 100 \right) \times 400\)
\(= \frac{3}{500} \times 400\)
\(= \frac{3 \times 400}{500} = \frac{1200}{500} = \frac{12}{5} = 2.4\)
In simple words: Remove the percentage sign by dividing by 100, then multiply by the given number.

Exam Tip: Be careful with percentages that are already fractions; divide by 100 accordingly.

Question 9. An article was bought for Rs 120 and sold for Rs 150. The gain/loss \(\%\) is
(i) \(25\%\) gain
(ii) \(30\%\) gain
(iii) \(25\%\) Loss
(iv) \(30\%\) gain
Answer: (i) \(25\%\) gain
Cost Price (CP) = Rs 120
Selling Price (SP) = Rs 150
Since SP > CP, there is a profit (gain).
Gain = \(\text{SP} - \text{CP} = 150 - 120 = \text{Rs } 30\)
Gain \(\%\) = \(\left( \frac{\text{Gain}}{\text{CP}} \right) \times 100\)
Gain \(\%\) = \(\frac{30}{120} \times 100 = \frac{1}{4} \times 100 = 25\%\)
In simple words: Profit percentage is always calculated on the cost price by finding the profit amount, dividing by cost price, and multiplying by 100.

Exam Tip: Profit and loss percentage are always computed with respect to the Cost Price unless specified otherwise.

Question 10. The S.I on Rs 500 for 2 years at \(2\frac{1}{2}\%\) is
(i) Rs 30
(ii) Rs 25
(iii) Rs 20
(iv) Rs 15
Answer: (ii) Rs 25
Principal (\(P\)) = Rs 500
Time (\(T\)) = 2 years
Rate (\(R\)) = \(2\frac{1}{2}\% = \frac{5}{2}\%\) per annum
Simple Interest (\(\text{S.I.}\)) = \(\frac{P \times R \times T}{100}\)
\(\text{S.I.} = \frac{500 \times \frac{5}{2} \times 2}{100}\)
\(\text{S.I.} = \frac{500 \times 5 \times 2}{2 \times 100} = \frac{5000}{200} = \text{Rs } 25\)
In simple words: Multiply Principal, Rate, and Time together, then divide by 100 to find the simple interest.

Exam Tip: Convert mixed fraction rates into improper fractions before applying the simple interest formula.