A alone can complete a job in 12 days and B alone in 18 days. A and B agree to do the work for ₹ 7,200. With C’s help they finish it in 5 days. How much should C be paid?
- (a)₹2,200
- (b)₹2,400
- (c)₹2,600
- (d)₹2,800
Answer
Why
Correct — A.
A's work in 5 days = 5 × 1⁄12 = 5⁄12
B's work in 5 days = 5 × 1⁄18 = 5⁄18
A and B together = 15⁄36 + 10⁄36 = 25⁄36
C's share of the work = 1 − 25⁄36 = 11⁄36
Pay follows work done: C gets 11⁄36 × ₹7,200 = ₹2,200 → option (a)
Why the others are wrong
- (b)₹2,400 — ₹2,400 is ₹7,200 ÷ 3, an equal split. Pay follows work, and C did 11⁄36 of the job, less than a third (12⁄36).
- (c)₹2,600 — ₹2,600 is 13⁄36 of ₹7,200. C would have to do 13⁄36 of the job, but A and B already finish 25⁄36 in the 5 days, leaving 11⁄36.
- (d)₹2,800 — ₹2,800 is 14⁄36 of ₹7,200. That leaves A and B only 22⁄36 of the work, yet in 5 days they do 25⁄36 between them.
Concept
When a group is paid one sum for one job, each person's pay is in the ratio of the work each did, not simply the days each worked. All three worked the same 5 days here, so the split follows their one-day rates.
Work done: A 5⁄12, B 5⁄18, C the rest. In 36ths that is 15 : 10 : 11, so the ₹7,200 splits as ₹3,000 : ₹2,000 : ₹2,200.
The ₹7,200 is the fee for the whole job, agreed before C joined. C's help does not raise it, so C is paid out of it for the share C did.
Key facts
- A person's one-day work is 1 ÷ (days they need alone).
- Payment for a shared job divides in the ratio of work done.
- Here A did 15⁄36, B 10⁄36 and C 11⁄36 of the job, earning ₹3,000, ₹2,000 and ₹2,200.
Study next
Common traps
- Splitting ₹7,200 equally among three people because all three worked the same 5 days.
- Splitting in the ratio of days needed alone: the fastest worker, A, earns the most, not the least.
19 Sep 2025, 16:00, Quant Q.5 splits ₹840 by work in the same way: B, twice as efficient as A, joins after 25% is done, so of the remaining 75% A does 25% and B 50%, and B's share is ₹420.
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