If the interest on ₹ 2,400 is more than the interest on ₹ 2,000 by ₹ 60 in 3 years at the same rate per cent, find the rate.

Given:

P₁ = ₹ 2,400

T₁ = 3 years

Let the rate be $r$.

Hence,

$\text{S.I.} = \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] \Rightarrow \text {S.I} = \Big(\dfrac{2,400 \times r \times 3}{100}\Big)\\[1em] \Rightarrow \text {S.I} = \Big(\dfrac{7,200r}{100}\Big)\\[1em] \Rightarrow \text {S.I} = 72r\\[1em]$

P₂ = ₹ 2,000

T₂ = 3 years

R = r%

$\text{S.I.} = \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] \Rightarrow \text{S.I.} = \Big(\dfrac{2,000 \times r \times 3}{100}\Big)\\[1em] \Rightarrow \text{S.I.} = \Big(\dfrac{6,000r}{100}\Big)\\[1em] \Rightarrow \text{S.I.} = 60r$

According to the question,

Difference between the two S.I. = ₹ 60

$72r - 60r = ₹ 60\\[1em] \Rightarrow 12r = ₹ 60\\[1em] \Rightarrow r = \dfrac{60}{12}\\[1em] \Rightarrow r = 5$

Hence, the rate is 5%.