Three people, A, B and C, invest in a business in the ratio 2 : 3 : 5. It was decided that 9% of the profits will go to charity. If the total profit was ₹2,50,000, then find the share of C in the profit (in ₹).
- (a)1,11,650
- (b)1,13,750
- (c)1,26,950
- (d)1,21,850
Answer
Why
Correct — B. Charity takes 9%, so the partners divide the remaining 91%.
Distributable profit = 0.91 × 2,50,000 = ₹2,27,500
C's ratio share = 5 ⁄ (2 + 3 + 5) = 5⁄10 = one half
C's profit = ½ × 2,27,500 = ₹1,13,750 → option (b).
Why the others are wrong
- (a)1,11,650 — ₹1,11,650 is below the correct share, which means more than 9% has been taken out. The deduction is exactly 9%, applied once, to the whole profit.
- (c)1,26,950 — ₹1,26,950 exceeds half of the gross ₹2,50,000, which is ₹1,25,000. C holds 5 of 10 parts, so C's share cannot beat half even before charity is deducted.
- (d)1,21,850 — ₹1,21,850 sits between the no-charity ₹1,25,000 and the correct ₹1,13,750, so only part of the 9% has been removed. The full 9% comes off first.
Concept
Profit divides in the ratio of capital when every partner's money stays in for the same length of time, which is the case here. The ratio 2 : 3 : 5 sums to 10 parts, so C takes 5 of 10 — exactly half of whatever reaches the partners.
The step the option list is built around is the charity deduction. It comes off the whole profit before the ratio is applied, so the pool is 91% of ₹2,50,000, which is ₹2,27,500, and half of that is ₹1,13,750.
The phrase 9% of the profits will go to charity means 9% of the total profit, taken before any partner is paid.
Deducting 9% from C's share after dividing gives the same ₹1,13,750 here, because the deduction is a flat percentage rather than a fixed rupee sum.
Key facts
- When capitals run for equal periods, profit divides in the capital ratio.
- 2 : 3 : 5 sums to 10 parts, so C's 5 parts are exactly half of the distributable profit.
- A charity or reserve deduction is taken from the whole profit before the ratio is applied.
- 91% of ₹2,50,000 is ₹2,27,500.
Study next
Common traps
- Dividing the full ₹2,50,000 and answering ₹1,25,000.
- Adding 2 + 3 + 5 as 9 and taking 5⁄9 of the distributable profit.
- Deducting 9% twice, once from the profit and again from C's share.
The ratio split is the straightforward half; the deduction that comes before it is what separates the options. A three-way ratio division of a fixed sum runs at 12 Sep 2024, 09:00, Quant Q.15, where ₹1,200 is divided 2 : 1 : 3.
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