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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 (in Rs.)?

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 (in Rs.)? Correct Answer Rs. 235200

Capital of A, B and C = 4 : 2 : 9

⇒ Suppose capital of A = 4

⇒ Suppose capital of B = 2

⇒ Suppose capital of C = 9

⇒ Total capital of A after end of the year = 4 × 3 + (4/2) × 3 + (4/4) × 3 + (4/8) × 3

= 12 + 6 + 3 + (3/2) = 45/2

⇒ Total capital of B after end of the year = 2 × 3 + 4 × 3 + 8 × 3 + 16 × 3 = 6 + 12 + 24 + 48

= 90

⇒ Total capital of C after end of the year = 9 × 12 = 108

⇒ Profit ratio of A, B and C = (45/2) : 90 : 108 = 5 : 20 : 24

⇒ 5 unit = 24000

⇒ 1 unit = 24000/5 = 4800

⇒ (5 + 20 + 24) unit = 49 unit = 4800 × 49 = Rs. 235200

⇒ Total profit = Rs. 235200

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