SSC CGL 2025 Tier-II · Paper-I, 19 January 2026 · Mathematical Abilities · Question 16 of 150

We transcribed this text from the pictures of a candidate's response sheet for this paper; the answer is the key SSC marked with a green tick on that sheet. Solution last reviewed 11 September 2026.

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A, B, and C invest in a business in the ratio 2:3:5. After 4 months, A increases his capital by 50%, B decreases his capital by 1⁄3, and C leaves the capital unchanged. At the end of the year, if the total profit is Rs. 33,000, find the share of B.

(a)Rs. 7,700
(b)Rs. 8,000
(c)Rs. 9,000
(d)Rs. 10,500

Answer

Why

Correct — A. Profit is shared in the ratio of capital × months (unit-months). Take the starting capitals as 2, 3 and 5 units.

After 4 months: A becomes 2 × 1.5 = 3, B becomes 3 × 2⁄3 = 2, C stays 5
A's unit-months: 2 × 4 + 3 × 8 = 32
B's unit-months: 3 × 4 + 2 × 8 = 28
C's unit-months: 5 × 12 = 60

Add: 32 + 28 + 60 = 120, so one unit-month earns 33,000 ÷ 120 = Rs. 275
B's share: 28 × 275 = Rs. 7,700 → option (a)

Why the others are wrong

(b)
Rs. 8,000 — Rs. 8,000 would need B to hold 8⁄33 of the 120 unit-months, about 29.1. B holds exactly 28: 12 in the first four months and 16 in the last eight.
(c)
Rs. 9,000 — Rs. 9,000 is 3⁄11 of the profit, a larger slice than B earns. B holds 28 of the 120 unit-months, which is 7⁄30, and 7⁄30 of 33,000 is Rs. 7,700.
(d)
Rs. 10,500 — Rs. 10,500 is more than B's starting slice, 3⁄10 × 33,000 = Rs. 9,900. B cut his capital while A raised his, so B's slice must shrink below 3⁄10, not grow.

Concept

In a partnership the profit is split in proportion to capital × time. Count it in unit-months: one unit of capital held for one month.

When a partner changes capital midway, split his year at the change and add the two products.

A percentage or fraction change acts on the partner's own capital: A's 50% rise turns 2 units into 3, and B's cut of 1⁄3 turns 3 units into 2.

Check: A gets 32 × 275 = Rs. 8,800 and C gets 60 × 275 = Rs. 16,500. With B's Rs. 7,700 the three add to Rs. 33,000.

Key facts

Profit ratio = ratio of (capital × months) for each partner.
A 50% increase multiplies a capital by 3⁄2.
A decrease of 1⁄3 multiplies a capital by 2⁄3, not by 1⁄3.
A change after 4 months of a 12-month year leaves the new capital in place for 8 months.

Study next

Partnerships where a partner joins late or leaves earlyWorking partners who draw a salary or commission before the profit is sharedFinding an unknown investment period from a given profit ratio

Common traps

Applying the new capitals for the whole year and ignoring the first four months at 2 : 3 : 5.
Reading 'decreases by 1⁄3' as 'decreases to 1⁄3', which turns B's 3 units into 1 instead of 2.

Here a ratio and two percentage changes stand in for rupee amounts.

A mid-period change of capital also decides 14 Sep 2025, 12:30, Quant Q.7, which starts from the same 2 : 3 : 5 ratio with two withdrawals over 18 months, and 15 Sep 2025, 16:00, Quant Q.4, where Kapil withdraws ₹40,000 six months in.

Related PYQs

No directly related past PYQ was found.

Topic: Profit and Loss — all 57 SSC CGL questions on it, every solved shift.