Question : A money lender lends Rs. 400 for 3 years to a person and lends Rs. 500 for 4 years to another person at the same rate of simple interest. If he receives Rs.160 as interest, what is the rate of interest per annum?
Option 1: 5%
Option 2: 7%
Option 3: 9%
Option 4: 10%
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Correct Answer: 5%
Solution :
Let the rate of interest per annum be $r$%.
We know, Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$
Here the interest for Rs. 400 for 3 years at $r$% rate is = $\frac{400×r×3}{100} = 12r$
and the interest for Rs. 500 for 4 years at r% rate is = $\frac{500×r×4}{100} = 20r$
So, $(12r+20r) = 160$
$\therefore r = \frac{160}{32} = 5\%$
Hence, the rate of interest per annum is 5%.
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