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## Explanation

A and B entered a partnership investing Rs. 16000 and Rs. 12000 respectively.

- A withdraw Rs. 5000, after 3 months.
- B invested Rs. 5000 more, after 3 months.
- Â C joins the business with a capital Rs. 21000, after 3 more months.

First, weâ€™ll calculate A and Bâ€™s investment for first 3 months (16000 x 3 = 48000 and 12000 x 3 = 36000).

After months; A withdraws 5000 (16000 â€“ 5000 = 11000) and B invests 5000 more (12000 + 5000 = 17000). Now investment of A and B for rest of the year (11000 x 9 = 99000 and 17000 x 9 = 153000).

So, total investment of A and B for 12 months (48000 + 99000 = 147000 and 36000 + 153000 = 189000).

After 6 months, C joins with capital of 21000 (21000 x 6 = 126000)

As, the ratio of profit equals the ratio of investment (A : B : C = 147000 : 189000 : 126000 and it would be reduced in its lowest form).

- Bâ€™s share in profit = (Bâ€™s ratio of investment x total profit)/total ratio

- Câ€™s share in profit = (Câ€™s ratio of investment x total profit)/total ratio

- Share of B exceeds that of C = Bâ€™s share in profit â€“ Câ€™s share in profit

## To Find

Share of B exceeds that of C = ?

## Solution

Investment of A for first 3 months = 16000 x 3 = 48000

Investment of B for first 3 months = 12000 x 3 = 36000

A withdraws 5000 after 3 months = 16000 â€“ 5000 = 11000

Investment of A for next 9 months = 11000 x 9 = 99000

- Total investment of A for 12 months = 48000 + 99000 = 147000

B invested 5000 more after 3 months when A withdraws 5000 = 12000 + 5000 = 17000

Investment of B for next 9 months = 17000 x 9 = 153000

- Total investment of B for 12 months = 36000 + 153000 = 189000

- C joins after 6 months with a capital of 21000 = 21000 x 6 = 126000

Now;

A : B : C = 147000 : 189000 : 126000

A : B : C = 147 : 189 : 126 (and 147 + 189 + 126 = 462)

Total profit = 26400

Bâ€™s share in profit = (189 x 26400)/462 = 10800

Câ€™s share in profit = (126 x 26400)/462 = 7200

Share of B exceeds that of C = 10800 â€“ 7200 = **Rs. 3600 answer**

## Conclusion

A and B entered a partnership investing Rs. 16000 and Rs. 12000 respectively. After 3 months, A withdraw Rs. 5000 while B invested Rs. 5000 more. After 3 more months, C joins the business with a capital Rs. 21000. The share of B exceeds that of C, out of total profit of Rs. 26400 after one year by is Rs. 3600.