A started a business investing Rs. 1400. After 5 months, B joined the business and after 2 months more, C and joined the business. If their proportiiona of profits after one year be `4:3:2`, then what amount of capitals had B and C invested in the business?

Explanation

The proportion of profits of A,B and C `=4:3:2`
`:.` The proportion of their capital `=4:3:2`
`:.` part of A's profit `=4/(4+3+2)=4/9`
part of B's profit `=3/(4+3+2)=3/9=1/3`
part of C's profit `=2/(4+3+2)=2/9`
Now A's capital in respect of 1 mont `=Rs. (1400xx12)`
`=Rs. 16800`
`:.4/9` part of the capital `=Rs. 16800`
`:.1/3.......................=Rs. 16800xx9/4xx1/3=Rs. 12600`
`:.2/9` ..............=Rs. `16800xx9/4xx2/9=Rs. 8400`
But B and C had invested capitals for 7 months and 5 months respectively.
`:.` Capital of `B= Rs. 12600-:Rs. 1800`
Capital of `C=Rs. 8400-:5=Rs. 1680`
`:.B` and C had invested Rs. 1800 and Rs. 1680 respectively in the business.