Question : A, B and C started a business with their capitals in the ratio 4 : 2 : 9. At the end of every quarter, A halves his capital, whereas B doubles his capital and C leaves his capital unchanged. If at the end of a year, A's profit was Rs. 24,000, then what is the total profit?
Option 1: Rs. 2,30,400
Option 2: Rs. 2,25,600
Option 3: Rs. 2,16,000
Option 4: Rs. 2,35,200
Correct Answer: Rs. 2,35,200
Solution :
The initial capitals of A, B, and C are in the ratio 4 : 2 : 9.
Let their initial capitals as 4k, 2k, and 9k respectively.
In a year, there are 4 quarters. At the end of every quarter, A halves his capital, B doubles his capital, and C leaves his capital unchanged. So, the total capital invested by A, B, and C in a year would be:
A: 4k + 2k + k + 0.5k = 7.5k
B: 2k + 4k + 8k + 16k = 30k
C: 9k + 9k + 9k + 9k = 36k
The profit is divided by the ratio of their investments. So, if A's profit is Rs. 24,000, then the total profit P can be calculated as:
⇒ P = $\frac{24000 }{ 7.5k}$ × (7.5k + 30k + 36k)
⇒ P = $\frac{24000 }{ 7.5k}$ × 73.5k
⇒ P = 1600 × 147
⇒ P = 2,35,200
Hence, the correct answer is Rs. 2,35,200.
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