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## Explanation

A, B and C enter into a partnership and their shares are in the ratio 1/2 : 1/3 : 1/4.

After 2 months, A withdraws half of his capital.

A : B : C = 1/2 : 1/3 : 1/4 multiplying it with suitable number alters it utterly (A : B : C = 6 : 4 : 3).

For first 2 months and next 10 months; A’s investment will be 12 and 30 respectively (total investment of A = 42)

48 and 36 will be the require investment of B and C for 12 months.

Now, ratio of profit equals ratio of investment (A : B : C = 42 : 48 : 36); total profit is given (378), so required share of B would be;

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

## To Find

B’s share in profit = ?

## Solution

Given ratio of investment of A, B and C = 1/2 : 1/3 : 1/4

A : B : C = 6 : 4 : 3

After 2 months A withdraws half of its investment;

For first 2 months = 6 x 2 = 12

For next 10 months = 3 x 10 = 30

Total investment of A for 12 months = 12 + 30 = 42

Investment of B for 12 months = 4 x 12 = 48

Investment of C for 12 months = 3 x 12 = 36

A : B : C = 42 : 48 : 36

A ; B : C = 7 : 8 : 6 (7 + 8 + 6 = 21)

B’s share in profit = (8 x 378)/21 = **Rs.** **144** **answer**

## Conclusion

A, B and C enter into a partnership and their shares are in the ratio 1/2 : 1/3 : 1/4. After 2 months, A withdraws half of his capital and after 10 months, a profit of Rs. 378 is divided among them. The required share of B would be Rs. 144.