A sum of money at simple interest amounts to Rs 1012 in \(2\frac{1}{2}\) years and to Rs 1067.20 in 4 years. Find the rate of interest and the sum.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 4%, Rs 920
Simple interest is the same every year, so the difference of the two amounts is the interest for the difference of the two times.
Interest for \(\displaystyle 4-2\frac{1}{2}=1\frac{1}{2}\) years \(=1067.20-1012=\) Rs 55.20
Interest for 1 year \(\displaystyle =\frac{55.20}{1.5}=\) Rs 36.80
Interest for \(2\frac{1}{2}\) years \(=2.5\times36.80=\) Rs 92
Sum \(=1012-92=\) Rs 920
Rate \(\displaystyle =\frac{36.80}{920}\times100=4\%\)
The rate is 4% and the sum is Rs 920.