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A, B and C start a business. A invests money for 4 months and claims \(\frac{1}{8}\) of the total Profit and B invests money for 6 months and claims \(\frac{1}{3}\) of the Profit while C invests Rs. 1560 for 8 months. How much money A & B invest?

A, B and C start a business. A invests money for 4 months and claims \(\frac{1}{8}\) of the total Profit and B invests money for 6 months and claims \(\frac{1}{3}\) of the Profit while C invests Rs. 1560 for 8 months. How much money A & B invest? Correct Answer A  → Rs. 720; B → Rs. 1280

Given:

A invests money for 4 months and claims 1/8 of total profit

B invests money for 6 months and claims 1/3 of total profit

C invests 1560 for 8 months

Calculation:

Ratio of Profit = 1/8 : 1/3 : (1 – (1/8) + (1/3))

⇒ Ratio = 1/8 : 1/3 : 13/24

⇒ 3 : 8 : 13

Now, for A and C

A × 4 : C × 8 = 3 : 13

A = (1560 × 8 × 3)/(4 × 13) = 720

For B and C,

B × 6 : C × 8 = 8 : 13

B = (1560 × 8 × 8)/(6× 13) = 1280

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