A,B and C invested Rs. 5000, Rs. 6000 and Rs. 4000 respectively in a business. A has taken 30% of the profit so as to manage the business and the rest of the profit is distributed among them in accordance with the of their capital. If after 1 year A has go Rs. 200 more than the aggregate of the profits of B and C, then the profits of each of them the total amount of profit.

Explanation

The ratio of the capitals of A,B and C `=5000:6000:4000=5:6:4`
`:.` Part of the capital of `A=5/(5+6+4)=5/15`
part of the capital of `B=6/15` and part of the capital fo `C=4/15`
Let the profit be Rs. `x` after 1 year.
As per question A will get `Rs. x xx30/100=Rs. (3x)/10` for management.
So the rest of the profit `=Rs. (x-(3x)/10)=Rs. (7x)/10`.
Now distributing according to the ratio of capitals from `Rs. (7x)/10`
A will get `Rs. (7x)/10xx5/15=Rs. (35x)/150` and B will get `Rs.(7x)/10xx6/15=Rs. (42x)/150`
and C will get `Rs.(7x)/10xx4/15=Rs. (28x)/150`
As per question `((3x)/10+(35x)150)-(42x)/150+(28x)/150)=200`
`implies (45x+35x)/150-(70 x)/150=200`
`implies(80x)/150-(70x)/150=200`
`implies(80x-70x)/150=200implies(10x)/150=200`
`impliesx=200xx15impliesx=3000`
So the total profit `=Rs. 3000`
Now the profit obtained by `A=Rs. ((3x)/10+(35x)/150)=Rs(945x+35x)/150)`
`=Rs. (80x)/150=Rs. (80xx3000)/150=Rs. 16000`
The profit obtained by `B=Rs. (42x)/150=Rs. (42xx3000)/150=Rs. 840`
and the profit obtained by `C=Rs. (28x)/150=Rs. (28xxx3000)/150=Rs. 560`
Hence, the total profit isRs. 30000 and the shares of A,B and C are Rs. 1600, Rs. 840 and Rs. 560 respectively.