A and B start a business with investments of Rs 40,000 and Rs 50,000 respectively. C joins them on the condition that the whole profit will be shared equally among the three. For this, C pays Rs 45,000 to A and B together. How much of this amount does B receive?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs 30,000
C pays A and B for the part of the profit each of them gives up, so the payment is shared in the ratio of those parts.
Old shares: A \(=\frac{4}{9}\), B \(=\frac{5}{9}\); new share of each \(=\frac{1}{3}=\frac{3}{9}\)
A gives up \(\frac{1}{9}\), B gives up \(\frac{2}{9}\)
Ratio of what they give up \(=1:2\)
B receives \(\displaystyle \frac{2}{3}\times45000=\) Rs 30,000
B receives Rs 30,000.
Why the other options are incorrect
Option (1) Rs 22,500 — Incorrect. This splits the payment equally between A and B.
Option (2) Rs 15,000 — Incorrect. This is A’s part of the payment, not B’s.
Option (4) Rs 25,000 — Incorrect. This shares the payment in the ratio of the capitals; it must be shared in the ratio of what each partner gives up.