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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. |
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Answer» 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. |
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