SSC CGL 2024 Tier-I · 24 September 2024, Shift 1 · Quantitative Aptitude · Question 24 of 98

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 10 September 2026.

Where this paper and its answers come from

SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

A, B and C invested money in a business such that 2 times A's share, 4 times B's share and 6 times C's share are all equal. If they earned ₹44,000, find the share of A.

(a)₹12,000
(b)₹22,000
(c)₹24,000
(d)₹20,000

Answer

Why

Correct — C. Equal products mean the shares are inversely proportional to the multipliers, so the partner with the smallest multiplier holds the largest share.

Set 2A = 4B = 6C = 12k (12 is the LCM of 2, 4 and 6):
A = 12k ÷ 2 = 6k
B = 12k ÷ 4 = 3k
C = 12k ÷ 6 = 2k

So A : B : C = 6 : 3 : 2, which is 11 parts.

One part = 44,000 ÷ 11 = ₹4,000
A's share = 6 × 4,000 = ₹24,000 → option (c).

Why the others are wrong

(a)
₹12,000 — ₹12,000 is B's share — 3 parts of the 6 : 3 : 2 split. A carries the smallest multiplier, so A takes the largest share, not the middle one.
(b)
₹22,000 — ₹22,000 is half of ₹44,000, which would need A to hold as much as B and C together. A holds 6 parts out of 11, not 1 out of 2.
(d)
₹20,000 — ₹20,000 is not a whole number of parts. One part is ₹4,000, so the only shares this split can produce are ₹24,000, ₹12,000 and ₹8,000.

Concept

When a stem equates multiples — 2A = 4B = 6C — it is giving you the ratio upside down. Bigger multiplier, smaller share.

The clean method is the LCM method. Set the common value to the LCM of the multipliers, 12, and divide it by each one: 12⁄2, 12⁄4, 12⁄6 gives 6 : 3 : 2 in whole numbers with no fractions on the page.

Equivalently A : B : C = 1⁄2 : 1⁄4 : 1⁄6, which is the same ratio before clearing denominators. Once the ratio is in parts, the money divides by parts.

The stem says the partners invested and then earned ₹44,000 together, with no separate time periods given, so profit divides in the same ratio as the shares. Checking the total is the fastest guard: 24,000 + 12,000 + 8,000 = 44,000.

Key facts

If 2A = 4B = 6C then A : B : C = 1⁄2 : 1⁄4 : 1⁄6 = 6 : 3 : 2.
The LCM method clears the fractions: divide the LCM of the multipliers by each multiplier.
With 11 parts sharing ₹44,000, one part is ₹4,000.
The three shares are ₹24,000, ₹12,000 and ₹8,000, which total ₹44,000.

Study next

Partnership where capitals stay in for unequal periods, so profit follows capital × monthsWorking and sleeping partners, where one takes a fee before the ratio appliesInverse proportion in time-and-work, where more men mean fewer days

Common traps

Reading 2A = 4B = 6C straight off as A : B : C = 2 : 4 : 6, which inverts the answer.
Splitting ₹44,000 three ways because there are three partners.
Finding the ratio correctly and then handing the 6 parts to C instead of A.

SSC also asks profit division on a stated ratio at 26 Sep 2024, 9:00, Quant Q.5, where A, B and C invest in the ratio 2 : 3 : 5 and 9% of the profit is set aside for charity before the split.

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