Rahamatchacha takes a loan amount of ₹ 240000 from a bank for constructing a building at the rate of simple interest of 12% per annum. After 1yr of taking the loan, he rents the house at the rate of ₹ 5200 per month. Let us determine the number of years he would take to repay his loan along with interest from the income of the house rent

Let after x years he will repayment the amount.

Interest of ₹ 240000 at 12% for x years

= \frac{240000 × 12 × x}{100} = 28800 x

Amount = Principal + Interest

= ₹ (240000+28800x)

Now, house rent for 1 year 12m = ₹ 5200 × 12

∴ House rent for (x – 1) yrs = ₹ 5200 × 12 × (x – 1)

= 62400 (x – 1)

According to the problem,

62400 (x – 1) = 240000 + 28800 x

or, 62400 x – 62400 = 240000 + 28800 x

or, 62400 x – 28800 x = 240000 + 62400

or, 33600 x = 302400

∴ x =\frac{302400}{33600}=9

∴ After 9 years he will repay his loan with interest.