Simple interest on a certain sum of money for 3 years at 8% per annum is half of the compound interest on ₹ 6000 for 2 years at 10% per annum. Find the sum on which simple interest is calculated?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → ₹ 2625
The compound interest on ₹6000 is worked out first; half of it is the simple interest, and the simple interest formula \(SI=\displaystyle\frac{P\times R\times T}{100}\) then gives the sum.
Compound interest on ₹6000 for 2 years at 10%:
Each year the amount grows by 10%, so after 2 years it is \(6000\times1.1\times1.1=7260\)
The interest is the growth over the principal: CI \(=7260-6000=1260\)
The sum (the simple interest is half the CI, ₹630):
Simple interest for 3 years at 8%: \(\displaystyle\frac{P\times8\times3}{100}=630\)
So the sum is \(\displaystyle P=\frac{630\times100}{24}=\) ₹2625