CSAT Solved Papers/ 2021/Q54

2021 CSAT — Q54

Quant Arithmetic & numeracy 2.5 marks Easy

$P$ scored $40$ marks more than $Q$ in an examination. If $Q$ scored $10\%$ less marks than $P$ , then how much did $Q$ score?

A 360 Answer
B 380
C 400
D 420

Worked rationale

Let $P$ ‘s score be $P$ . Two facts:

Q = P - 40 \qquad\text{and}\qquad Q = 0.90\,P\ \ (\text{“}10\%\text{ less than }P\text{”}).

Set them equal:

0.90P = P - 40 \;\Rightarrow\; 0.10P = 40 \;\Rightarrow\; P = 400.

Then $Q = 0.90 \times 400 = 360$ .

Answer: (a) 360.

Why the other options miss

B

an arithmetic slip: solves $P=400$ but reports $P-20$ or takes $10\%$ of a wrong base.
C

answered the sub-step, not the question: stops at $P = 400$ and reports $P$ ‘s score instead of $Q$ ‘s.
D

wrong base for the percentage: takes ” $10\%$ less” on $Q$ ‘s base, writing $P = 0.9Q$ and back-solving wrongly.

Specialist insight

” $10\%$ less than $P$ ” must be read on $P$ ‘s base, i.e. $Q = 0.9P$ — that’s the whole game. Combine with $Q = P - 40$ to get $0.1P = 40$ , so $P = 400$ and $Q = 360$ . Two traps sit in plain sight: the base of the percentage (it’s $P$ , not $Q$ ) and the final read-off (the question wants $Q$ , not $P$ ). State both equations explicitly before solving so neither slips.

The trap, in one line

$0.9P = P-40 \Rightarrow P=400 \Rightarrow Q = 360$ (answer is $Q$ , not $P$ ) $\Rightarrow$ (a).

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