A, B and C invest in a business for the same period, and \(\frac{1}{3}\) of A’s capital \(=\) \(\frac{1}{4}\) of B’s capital \(=\) \(\frac{2}{5}\) of C’s capital. Out of a total profit of Rs 11,400, find B’s share.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Rs 4,800
If equal fractions of the capitals are the same amount \(k\), each capital is \(k\) divided by its fraction, so the capitals are in the ratio of the reciprocals.
A \(=3 k\), B \(=4 k\), C \(=\frac{5}{2} k\)
A : B : C \(=6:8:5\), total 19 parts
B’s share \(\displaystyle =\frac{8}{19}\times11400=\) Rs 4,800
B’s share is Rs 4,800.
Why the other options are incorrect
Option (2) Rs 3,000 — Incorrect. This is C’s share, not B’s.
Option (3) Rs 3,600 — Incorrect. This is A’s share, not B’s.
Option (4) Rs 3,800 — Incorrect. This splits the profit equally; the capitals are not equal.