Three friends, investing Rs. 120000, Rs. 150000 and Rs. 110000, bought a bus. One friend is a driver and the rest two friends are conductors. They decied that `2/5` th of the gain will be distributed amongst themselves at the ratio `3:2:2` due to their corresponding works and the rest at the ratio of their respective capitals. If the profit of a month be Rs. 29260, then find the amount of profit of each of them.

Explanation

The ratio of capitals of three friends `=20000: 150000:110000=12:15:11`
`:.` The part of the capital of first fried `=12/(12+15+11)=12/38`
The part of the capital of second friend `=15/(12+15+11)=15/38`
and the part of the capital of third friend `=11/(12+15+11)=11/38`
Profit of 1 month `=Rs. 29260`
Profit distributed according to theri respective works `=Rs. 29260xx2/5=Rs. 11704`
The ratio of the profits due ot works `=3:2:2`
`:.` From Rs. 11704, the first friend, i.e. the driver will get Rs. `11704xx3/7=Rs. 5016`
Also the second and the third friend i.e. the conductors will get each Rs. `11704xx2/7=Rs. 3344`
The profit distributed according to the ratio of their respective capitals `=Rs. (29260-11704)`
`=Rs. 17556`
`:.` In Rs. 17556 the first friend i.e. the driver will get Rs. `17556xx12/38=Rs. 5544`
The second friend will get `Rs. 17556xx15/38=Rs. 6930`
and the third friend will get `Rs. 17556xx11/38=Rs. 5082`
`:.` The total profit of of the first friend `=Rs. (5016+5544)=10560`
The total profit of the second friend `=Rs. (3344+6930)=Rs. 10274`
The total profit of the third friend `=Rs. (3344+5082)=Rs. 8426`
Hence the three friends will get profit Rs. 10560, Rs. 10274 and Rs. 8426 respectively.