A, B and C are partners in a business. A, whose money was used for 4 months, claims \(\frac{1}{8}\) of the profit. B, whose money was used for 6 months, claims \(\frac{1}{3}\) of the profit. C invested Rs 1,560 for 8 months. How much money did A and B contribute respectively?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs 720, Rs 1,280
Each partner’s share of the profit is in proportion to his capital × months. C’s figures are fully known, so they fix the value of one part of the profit.
C’s share \(\displaystyle =1-\frac{1}{8}-\frac{1}{3}=\frac{24-3-8}{24}=\frac{13}{24}\)
C: \(1560\times8=12480\) for 13 parts (of 24), so 1 part \(=960\)
A: \(\frac{1}{8}=\frac{3}{24}\), so capital × months \(=3\times960=2880\); capital \(\displaystyle =\frac{2880}{4}=\) Rs 720
B: \(\frac{1}{3}=\frac{8}{24}\), so capital × months \(=8\times960=7680\); capital \(\displaystyle =\frac{7680}{6}=\) Rs 1,280
A contributed Rs 720 and B contributed Rs 1,280.