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A and B Entered into a Partnership with Capitals in the Ratio 4:5. After 3 Months, A Withdrew 1/4 of his Capital and B Withdrew 1/5 of his Capital. The Gain at the End of 10 Months was Rs. 760. A’s Share in This Profit is?

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Explanation

A and B entered into a partnership with capitals in the ratio 4:5.

  • A withdrew 1/4 of his capital, after 3 months.
  •  And B withdrew 1/5 of his capital, after 3 months.

Now;

  • A’s investment for first 3 months will be 12 (4 x 3 = 12). But A takes 1/4 of his investment back (4 x 1/4 = 1), so remaining investment (4 – 1 = 3) for rest of period [(3 x 7) = 21] will be 21. This makes sense of total investment of A for 10 months [12 + 21 = 33] is 33.
  • B’s investment for first 3 months will be 15 (5 x 3 = 15). But B takes 1/5 of his investment back (5 x 1/5 = 1), so remaining investment (5 – 1 = 4) for rest of period [(4 x 7) = 28] will be 28. This makes sense of total investment of B for 10 months [15 + 28 = 43] is 43.

Now, ratio of profit equals ratio of investment (A : B  = 33 : 43); total profit is given (760), so required share of A would be Rs. 330.

A’s share in profit = (A’s ratio of investment x total profit)/total ratio

To Find

A’s share in profit = ?

Solution

Given ratio of investment of A and B = 4:5

  • A’s investment for first 3 months = 4 x 3 = 12
  • After 3 months, A takes back 1/4 of his initial investment = 4 x 1/4 = 1
  • Remaining investment of A = 4 – 1 = 3
  • Remaining investment of A for next 7 months = 3 x 7 = 21
  • Total investment of A for 10 months = 12 + 21 = 33

Now;

  • B’s investment of first 3 months = 5 x 3 = 15
  • After 3 months, B takes back 1/5 of his initial investment = 5 x 1/5 = 1
  • Remaining investment of B = 5 – 1 = 4
  • Remaining investment of B for next 7 months = 4 x 7 = 28
  • Total investment of B for 10 months = 15 + 28 = 43

A:B = 33:43    (33 + 43 = 76)

Total profit (given) = 760

A’s share in profit = (33 x 760)/76 = Rs. 330 answer

Conclusion

A and B entered into a partnership with capitals in the ratio 4:5. After 3 months, A withdrew 1/4 of his capital and B withdrew 1/5 of his capital. The gain at the end of 10 months was Rs. 760. A’s share in this profit will be Rs. 330.

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