Question

Arun lent Rs 5,000 to Balaji for 2 years and Rs 3,000 to Charles for 4 years on simple interest at the same rate of interest and received Rs 2,200 in all from both of them as interest. Find the rate of interest per year.

Answer 1

Principal lent to Balaji P₁ = Rs 5000 

Time n₁ = 2 years 

Let r be the rate of interest per year 

Simple interest got from Balaji = \(\frac{pnr}{100}\)

⇒ I₁ = \(\frac{5000\times25\times\,r}{100}\)

Again principal let to Charles P₂ = Rs 3000 

Time (n₂) = 4 years

Simple interest got from Charles (I₂) = \(\frac{3000\times4\times\,r}{100}\)

Altogether Arun got Rs 2200 as interest. 

∴ I₁ + I₂ = 2200 

\(\frac{5000\times25\times\,r}{100}\) + \(\frac{3000\times4\times\,r}{100}\) = 2200 

100r + 120r = 2200 

220r = 2200 

r = \(\frac{2200}{220}\)

 = 10 % 

Rate of interest per year = 10 %