A, B and C invested in a scheme in the ratio 4 : 7 : 6. Three months after the start, A gave half of his capital to B. Eight months after the start, C increased his capital by 50%. Out of a total profit of Rs 1,440 at the end of the year, find A’s share (in Rs).
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 200
Profit is shared in the ratio of capital × months. When the capital changes during the year, each amount is multiplied by the months for which it stayed, and the parts are added. The half that A hands over adds to B’s capital.
Let the capitals be \(4x\), \(7x\) and \(6x\)
A: \(4x\) for 3 months, then \(2x\) for 9 months; total \(12x+18x=30x\)
B: \(7x\) for 3 months, then \(7x+2x=9x\) for 9 months; total \(21x+81x=102x\)
C: \(6x\) for 8 months, then \(9x\) for 4 months; total \(48x+36x=84x\)
A : B : C \(=30:102:84\), total 216
A’s share \(\displaystyle =\frac{30}{216}\times1440=200\)
A’s share is Rs 200.