SSC CGL 2025 Tier-I · 15 September 2025, Shift 3 · Quantitative Aptitude · Question 4 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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Kapil invested ₹1,00,000 in a business. After 3 months, Manish joined with ₹80,000. After 3 more months, Kapil withdrew ₹40,000. Find their profit ratio at the end of the year.

(a)4:3
(b)2:3
(c)1:3
(d)5:3

Answer

Why

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

Kapil, months 0 to 6: 1,00,000 × 6 = 6,00,000
Kapil, months 6 to 12 after withdrawing ₹40,000: 60,000 × 6 = 3,60,000
Add Kapil's two periods: 6,00,000 + 3,60,000 = 9,60,000

Manish joins at month 3 and stays 9 months: 80,000 × 9 = 7,20,000

Ratio: 9,60,000 : 7,20,000 = 96 : 72 = 4 : 3 → option (a)

Why the others are wrong

(b)
2:3 — 2 : 3 gives Manish the bigger share, but Manish's 7,20,000 capital-months are fewer than Kapil's 9,60,000. Kapil's side of the ratio must be the larger.
(c)
1:3 — 1 : 3 would need Kapil's capital-months to be 2,40,000, a third of Manish's 7,20,000. Kapil's first six months alone come to 6,00,000.
(d)
5:3 — 5 : 3 ignores the withdrawal. Kapil's full ₹1,00,000 for 12 months is 12,00,000, and 12,00,000 : 7,20,000 = 5 : 3. After month 6 he has only ₹60,000 in.

Concept

In a partnership, profit is divided in the ratio of capital × time. Call the product capital-months.

A partner who joins late, or withdraws part of his money, is counted period by period. Split his year wherever his capital changes, multiply each amount by the months it stayed, and add the pieces.

The timeline has three breakpoints: month 0 (Kapil starts), month 3 (Manish joins) and month 6 (Kapil withdraws ₹40,000).

'After 3 more months' counts from Manish's joining, which is what puts the withdrawal at month 6.

Key facts

Profit ratio = ratio of each partner's capital × months.
A partner who withdraws mid-year contributes (original capital × months before) + (reduced capital × months after).
A partner who joins after 3 months of a 12-month year is counted for 9 months.

Study next

Partnership with three partners joining or withdrawing at different timesFinding one partner's share of a given profit from capital-monthsPartnership where a working partner takes a fixed cut before the split

Common traps

Placing the withdrawal at month 3 instead of month 6. 'After 3 more months' counts from Manish's joining.
Using Kapil's ₹1,00,000 for the full year and forgetting the ₹40,000 withdrawal.

14 Sep 2025, 12:30, Quant Q.5 has the same join-then-withdraw timeline: Sohan's 90,000 × 8 + 60,000 × 4 = 9,60,000 against Rohan's 1,50,000 × 7 = 10,50,000 gives 32 : 35.

14 Sep 2025, 12:30, Quant Q.7 applies capital × months across two withdrawals and 18 months, and gets 3 : 3 : 5.

Related PYQs

No directly related past PYQ was found.

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