In a partnership business, Amal invested Rs. 600 more than Bimal. Bimal invested for `7 1/2` months and Amal invested for 2 months more than Bimal. Now, if the profit of the business be Rs. 620 and Bimal got Rs. 140 less than Amal, find the capitals of Amal and Bimal.

Explanation

Let capital of Bimal be Rs. x
`:.` Capital of Amal is `Rs. (x+600)`
`:.` Bimal's investment in `7 1/2` months `=Rs. X xx 7 1/2=Rs. (15x)/2`
Also Amals investemet in `(7 1/2+2)` months `=9 1/2` months
is `Rs. (x+600)xx 19/2`
`=Rs. (19(x+600))/2`
`:.` (Capital of Amal): (Capital of Bimal)`=(19(x+600))/2:(15x)/2`
`=19(x+600):15x`......1
The total profit is Rs. 620
Let Amal has gto Rs. y
`:.` Bimal has got Rs. `(y-140)`
`:.y+y-140=620implies2y=620+140`
`implies2y=760`
`impliesy=760/2=380`
`:.` The profit obtained by Amal `=` Rs. 380 and the profit obtained by Bimal `=Rs. (620-380)=Rs. 240`
So, Amal's profit : Bimal's profit `=380:240=19:12`
`:.` Ratio of their capitals `=19:12`
`implies19(x+600):15x=19:12`
`implies(19(x+600))/(15x)=19/12implies15x=12(x+600)`
`implies15x=12x+7200`
`implies3x=7200impliesx=2400`
`:.` Capital of Bimal `=Rs. 2400` and capital of Amal `=Rs. (2400+600)=Rs. 3000`