A gives some money to `B` at a rate of `5%` and to `C Rs800` more at a rate of `7%` per annum. They repaid both the loans after `5` years and so that `C` have to pay `1240Rs` more than `R`. Find the quantities of money which both of them had debted.

Explanation

Let `A` have given a loan of `Rs x` to `B` and `Rs(x+800)` to `C`.
`:.` The simple interest of `Rs x` in `5` years at the rate of `5%` per annum `=Rs(x xx5xx5)/(100)=Rs(x)/(4)`
`:. B` have to pay `Rs(x+(x)/(4))=Rs(5x)/(4)` after `5` years.
Again, the simple interest of `Rs(x+800)` in `5` years
at the rte of `7%` per annum `=Rs((x+800)xx7xx5)/(100)`
`=Rs(35(x+800))/(100)=Rs(35x+28000)/(100)`
`:.` C have to pay `Rs{x+800+(35(x+800))/(100)}`
`=Rs(100x+80000+35x+28000)/(100)`
`=Rs(135x+108000)/(100)` after `5` years
As per question, `(135x+108000)/(100)-(5x)/(4)=1240`
`implies(135x+108000-125x)/(100)=1240`
`implies10x+108000=124000`
`implies10x=124000-108000`
`implies10x=16000impliesx=1600`
`:. B` had debted Rs. `1600` and `C` had debted `Rs(1600+800)=Rs2400`