GATE 2022 EC GA Q.2: solution and answer

GATE 2022 · ECGA Q.2 · 1 mark · MCQ

A sum of money is to be distributed among P, Q, R, and S in the proportion 5 : 2 : 4 : 3, respectively.

If R gets Rs. 1000 more than S, what is the share of Q (in Rs.)?

(A)
500
(B)
1000
(C)
1500
(D)
2000

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Answer and solution

ANSWER

Q's share is Rs. 2000, which is option (D).

Official answer: DSource: Official answer key, GATE 2022 EC (IIT Kharagpur)

Shares in a given ratio are all multiples of one common unit. Let P, Q, R and S get $5 k$ , $2 k$ , $4 k$ and $3 k$ rupees, for some $k > 0$ .
The difference between two shares is the difference of their ratio terms times $k$ : $R - S = 4 k - 3 k = k$ .
We are told R gets Rs. 1000 more than S, so $R - S = 1000$ , which gives $k = 1000$ .
Q's share is $2 k = 2 \times 1000 = 2000$ , so Q gets Rs. 2000. That is option (D).
Check: the shares are Rs. 5000, 2000, 4000 and 3000 (ratio $5 : 2 : 4 : 3$ ), and R gets $4000 - 3000 = 1000$ rupees more than S, as the question requires.

KEY IDEA

In a ratio split, every share is (its ratio term) × (one common unit $k$ ). A given difference between two shares fixes $k$ straight away: $R - S = (4 - 3) k = k = 1000$ . You do not need the total sum at all.

WATCH OUT FOR

Treating the Rs. 1000 difference as if it were the whole sum and dividing it in the ratio (which gives $\frac{2}{14} \times 1000 \approx 143$ , not an option). Another slip is to stop at $k = 1000$ and pick option (B), forgetting that Q's share is $2 k$ , not $k$ .

From the GATE 2022 EC paper. Every question of this paper · Download the full paper · All 58 Numerical questions, with notes

GATE 2022 EC GA Q.2: solution and answer

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