2021 CSAT — Q9

Quant Arithmetic & numeracy 2.5 marks Medium

In a class, $60\%$ of students are from India and $50\%$ of the students are girls. If $30\%$ of the Indian students are girls, then what percentage of foreign students are boys?

A 45%
B 40%
C 30%
D 20% Answer

Worked rationale

Take a base of $100$ students. Indian $=60$ , Foreign $=40$ , total girls $=50$ .

Indian girls $= 30\%$ of $60 = 18$ . So the remaining girls are foreign:

\text{Foreign girls} = 50 - 18 = 32.

Foreign students $=40$ , so foreign boys $= 40 - 32 = 8$ . As a percentage of foreign students:

\frac{8}{40}\times 100 = 20\%.

Answer: (d) 20%.

Visual solution

The same solve, worked by hand — read it, then trace it.

Hand-drawn worked solution for UPSC 2021 CSAT Q9 — Arithmetic & numeracy — Tap the drawing to open it full size for the fine detail.

Why the other options miss

A

wrong base for the percentage: takes foreign boys $8$ against the wrong denominator (e.g. out of the whole class rather than the $40$ foreigners).
B

answers a different question: reports the foreign share of the class ( $40\%$ ) rather than the boys-among-foreign figure asked.
C

wrong figure reused: lifts the ” $30\%$ of Indians are girls” number and reapplies it to foreigners.

Specialist insight

A $2\times 2$ table (India/Foreign $\times$ Girl/Boy) makes this a one-pass fill-in: anchor the row totals ( $60,40$ ) and the girls column total ( $50$ ), drop in Indian girls ( $18$ ), and every other cell follows by subtraction. The single trap is the base: the question asks for boys as a percentage of foreign students, so the denominator is $40$ , not $100$ . Always re-read which subtotal the “percentage of” is taken on before dividing.

The trap, in one line

Foreign boys $=40-(50-18)=8$ , and $8/40=20\%$ of foreigners $\Rightarrow$ (d) — not $8/100$ .

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