Two friends invested Rs. 40000 and Rs. 50000 respectively to start a business. They made a contract that they would divide 50% of the profit equally between themselves and the remining profit in the Ratio of the their capitals. Calculate the share of profit of the first friend if it is Rs. 800 less than that of the second friend.

Explanation

The ratio of capitals of the two two friends `=40000:50000=4:5`
So the part of the capital of the first friend `=4/(4+5)=4/9`
and the part of the capital of the second friend `=5/9`
Let the profit be Rs. `x`
So Rs. `x/2` is distributed equally between the two friends. So each friend gets `Rs. (x/2)/2=Rs. x/4`
Again Rs. `(x-x/2)=Rs. x/2` is distributed according to the ratio of their capitals.
`:.` From this Rs. `x/2` the first friend will get `Rs. x/2xx5/9=Rs. (5x)/18`
As per question `((5x)/14+x/4)-((4x)/14+x/4)=800`
or `(5x)/17-(4x)/18=800`
or `(5x-4x)/14=800`
or `x=800xx18`
or `x=14400`
`:.` The total profit `=Rs. 14400`
So the first friend will get profit `Rs. ((4x)/18+x/4)`
`=Rs. ((4xx14400)/18+14400/4)=Rs. (3200+3600)=Rs. 6800`
Hence the profit of the first friend will be Rs. 6800.