Question

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

Answer 1

Principal lent to Balaji P₁ = ₹ 5000

Time n₁ = 2 years

Let r be the rate of interest per year

Simple interest got from Balaji = ${\displaystyle \frac{\text{Pnr}}{100}}$

⇒ I₁ = ${\displaystyle \frac{5000\times 2\times \text{r}}{100}}$

Again principal let to Charles P₂ = ₹ 3000

Time (n₂) = 4 years

Simple interest got from Charles (I₂) = ${\displaystyle \frac{3000\times 4 \times \text{r}}{100}}$

Altogether Arun got ₹ 2200 as interest.

∴ I₁ + I₂ = 2200

${\displaystyle \frac{5000\times 2\times \text{r}}{100}+\frac{3000\times 4\times \text{r}}{100}}$ = 2200

100r + 120r = 2200

220r = 2200

r = ${\displaystyle \frac{2200}{220}}$

r = 10%

Rate of interest per year = 10%