SSC CGL 2025 Tier-I · 12 September 2025, Shift 3 · Quantitative Aptitude · Question 5 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 11 September 2026.

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A and B invested ₹1,20,000 and ₹1,60,000 respectively. A remained for 10 months and B for 7 months. What is the total profit if B's share is ₹16,800?

(a)₹34,800
(b)₹34,000
(c)₹10,000
(d)₹10,500

Answer

Why

Correct — A. Profit is shared in the ratio of capital × months.

A: 1,20,000 × 10 = 12,00,000
B: 1,60,000 × 7 = 11,20,000
Ratio A : B = 120 : 112 = 15 : 14

B's 14 parts = ₹16,800, so 1 part = 16,800 ÷ 14 = ₹1,200
Total = 15 + 14 = 29 parts = 29 × 1,200 = ₹34,800 → option (a)

Why the others are wrong

(b)
₹34,000 — Test it: B's 14⁄29 of ₹34,000 is about ₹16,414, not the ₹16,800 the stem gives. ₹34,000 is ₹800 short of the total.
(c)
₹10,000 — ₹10,000 is less than B's own ₹16,800. A total profit cannot be smaller than one partner's share, and A's share here is ₹18,000.
(d)
₹10,500 — ₹10,500 fails the same size test: it is ₹6,300 short of B's share alone, before A's ₹18,000 is even added.

Concept

In a partnership, profit is shared in the ratio of capital × time, the rupee-months each partner puts in. If both stay the same number of months, this reduces to the capital ratio.

Once the ratio is known, one partner's share fixes the value of one part. The total profit is that part multiplied by the sum of the ratio terms.

Options (c) and (d) are smaller than B's own share, so a size check leaves (a) and (b) before any division.

Key facts

Profit share is proportional to capital × months invested.
₹1,20,000 × 10 : ₹1,60,000 × 7 = 12,00,000 : 11,20,000 = 15 : 14.
A's share = 15 × ₹1,200 = ₹18,000, and ₹18,000 + ₹16,800 = ₹34,800.

Study next

Partners who join or withdraw capital partway through the yearA working partner's salary or commission taken out before the profit is splitFinding the months or the capital when the profit ratio is given

Common traps

Using the capital ratio 3 : 4 alone and ignoring the months, which gives a total of ₹29,400.
Stopping at A's share, ₹18,000, when the question asks for the total profit.

Here the partners stay for different months and B's share is given, so you work back to the total.

Capital × months also decides 12 Sep 2025, 09:00, Quant Q.6: ₹80,000 for 9 months against ₹1,20,000 for 6, an equal split.

It decides 15 Sep 2025, 16:00, Quant Q.5 too: ₹60,000 for 10 months against ₹90,000 for 8.

Related PYQs

No directly related past PYQ was found.

Topic: Profit and Loss — all 56 SSC CGL questions on it, every solved shift.