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## Explanation

In a partnership, A invests 1/6 of the capital for 1/6 of the time.

B invests 1/3 of the capital for 1/3 of the time.

and C, the rest of the capital for the whole time.

- Supposing the total investment ‘y’ for time ‘z’; it discloses A’s investment (y/6) for 1/6 of the time (z/6).

- Similarly; B’s 1/3 investment (y/3) for 1/3 of the time (z/3).

- Third companion is C, whose investment can be calculate by adding A and B’s investment (y/6 + y/3 = y/2) and subtracting it from total investment (y – y/2 = y/2). And time frame of investment of C is z (as given in the question i.e. C invests rest of the capital for the whole time).

Now;

- Total investment of A for duration of z/6 [(y x z)/(6 x 6) = yz/36] will be yz/36.

- Likewise B’s total investment for duration of z/3 [(y x z)/(3 x 3) = yz/9] will be yz/9.

- And C’s total investment for duration of z [(y x z)/2 = yz/2] will be yz/2.

As, ratio of profit depends upon the ratio of investment (A : B : C = yz/36 : yz/9 : yz/2); total profit is given (4600), so required share of B would be Rs. 800.

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

## To Find

B’s share in profit = ?

## Solution

Let suppose;

Total capital = y

Total time = z

- A invests 1/6 of the capital = y/6

- B invests 1/3 of the capital = y/3

- C invests rest of the capital = y – (y/6 + y/3) = y – y/2 = y/2

Now;

- A invests y/6 for 1/6 of the time = z/6

- B invests y/3 for 1/3 of the time = z/3

- C invests y/2 for the whole time = z

Total investments;

- Total investment of A for a specified time = (y x z)/(6 x 6) = yz/36

- Total investment of B for a specified time = (y x z)/(3 x 3) = yz/9

- Total investment of C for a specified time = (y x z)/2 = yz/2

A : B : C = yz/36 : yz/9 : yz/2

A : B : C = 1/36 : 1/9 : 1/2

A : B : C = 1 : 4 : 18 (1 + 4 + 18 = 23)

B’s share in profit = (4 x 4600)/23 = **Rs.** **800** **answer**

## Conclusion

In a partnership, A invests 1/6 of the capital for 1/6 of the time. B invests 1/3 of the capital for 1/3 of the time and C, the rest of the capital for the whole time. Out of a profit of Rs. 4600, B’s share is Rs. 800.