Rahamatchaha takes a loan amount of `2,40,000Rs` from a bank for constructing a building at the rate of simple interest of `12%` per annum. After `1` year of taking the loan he rents the house at the rate of `5200Rs` per month. Then, determine the number of years he would take to repay his loan along with interest from the income of the houserent.

Explanation

Let Rahamatchacha repay his loan along with interest after `x` years of the construction of the building.
Now, the houserent per month `=Rs5200`
`:.` Houserent of `1` year `=Rs5200xx12`
`:.` Houserent of `x` years `=Rs5200xx12xx x`.
Since, the house was rented after `1` years.
`:.` The loan was repaid after `(x+1)` years.
Now, the simple interest of `Rs240000` in `(x+1)` years
`=Rs(240000xx12xx(x+1))/(100)`
`=Rs2400xx12(x+1)`
`:.` Amount `=Rs{240000+2400xx12(x+1)}`
`=Rs2400[100+12x+12]`
`=Rs2400(112+12x)`
`:.2400(112+12x)=5200xx12x`
`implies112+12x=(5200xx12x)/(2400)`
`implies112+12x=26ximplies26x-12x=112`
`implies14x=112`
`impliesx=(112)/(14)=8`
`:.` The required time `=(8+1)` years `=9` years.