At the beginning of a year A, B and C jointly started a business. A invested `1/3` part of the capital and B invested an amount eqwual to the total capital of A and C. If the profit be Rs. 840 at the end of the year, then find the profits of each of them.

Explanation

Let the capital be Rs. `x`
So A invested `Rs. x/3` and the investement of B and C is `Rs.(x-x/3)=Rs. (2x)/3`………..1
As per question the investment of `B=Rs. x/3+` investment of C
`implies` (Capital of B)`-` (Capital of C)`=Rs. x/3`…….2
Now adding 1 and 2 we get `2xx("Capital of B")=((2x)/3)+x/3)=Rs. x`
`:.` Capital of `B=Rs. x/2`
`:.` From 1 we get capital of `C=Rs. ((2x)/3-x/2)=Rs. x/6`
So (Capital of A: (capital of B): (capital of C)`=x/3:x/2:x/6=1/3:1/2:1/6=2:3:1`
`:.` The part of the capital of `A=2/(2+3+1)=2/6`
The part of the capital of `B=3/6` and the part of the capital of `C=1/6`
So from Rs. 840 A will get `Rs. 840xx2/6=Rs. 280`
B will get RKs. `840xx3/6=Rs. 420` and C will get Rs. `840xx1/6=Rs. 140`
Hence the profits of A,B and C are Rs. 280, Rs. 420 and Rs. 140 respectively.