Actual CMAT questions on this topic from past papers, newest first. Each links back to its paper.
If a% of a + b% of b = 2% of ab, then what percent of a is b?
Answer: D
Given: a% of a + b% of b = 2% of ab.
\( \frac{a^2}{100} + \frac{b^2}{100} = \frac{2ab}{100} \)
\( a^2 + b^2 - 2ab = 0 \), so \( (a-b)^2 = 0 \).
This gives a = b, so b is 100% of a.
Answer: 100%
Arrange the following in increasing order:
A) 16 (2/3) %
B) 2/15
C) 0.17
D) 0.25 % of 64
Choose the correct answer from the options given below:
Answer: A
Convert everything to decimals:
Increasing order: 0.1333 < 0.16 < 0.1667 < 0.17, so B < D < A < C.
Answer: B < D < A < C (option 1)
If the cost price is 80% of the selling price, then what is the profit in percentage?
Answer: B
Asked: profit % when CP is 80% of SP.
Key idea: profit % is always calculated on the cost price.
Let SP = 100. Then CP = 80.
Profit = 100 − 80 = 20.
Profit % = \( \frac{20}{80} \times 100 = 25\% \).
Common trap: 20% is the profit as a share of the selling price (20 out of 100). That is not the profit percentage.
Faster: SP/CP = 100/80 = 5/4. So SP is 1/4 more than CP, which means 25% profit.
Answer: 25% (option 2)
In a local election between two candidates, one candidate got 55% of the total valid votes and was declared as winner. 15% of the votes were invalid. If the total number of votes polled were 15200, what were the valid votes of the loser:
Answer: C
Asked: the valid votes of the loser.
15% of the votes are invalid, so valid votes = 85% of 15200 = 12920.
The winner got 55% of the valid votes, so the loser got 45%.
Loser's votes = 0.45 × 12920 = 5814.
Shortcut: 0.85 × 0.45 × 15200 = 0.3825 × 15200 = 5814.
Answer: 5814
