What sum of money lent at 6.5% per annum will produce the same interest in 4 years as ₹ 7,500 produce in 6 years at 5% per annum?

Given:

P₁ = ₹ 7,500

R₁ = 5%

T₁ = 6 years

So, S.I.₁ =

$\text{S.I.} = \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] = \Big(\dfrac{7,500 \times 5 \times 6}{100}\Big)\\[1em] = \dfrac{2,25,000}{100}\\[1em] = 2,250$

R₂ = 6.5%

T₂ = 4 years

Let P₂ be $P$.

And S.I.₂ =

$\text{S.I.} = \Big(\dfrac{P \times R \times T}{100}\Big)\\[1em] = \Big(\dfrac{P \times 6.5 \times 4}{100}\Big)\\[1em] = \dfrac{26P}{100}\\[1em]$

As interest on both are same. Hence,

S.I.₁ = S.I.₂

$\therefore 2,250 = \dfrac{26P}{100}\\[1em] \Rightarrow P = \dfrac{2,250 \times 100}{26}\\[1em] \Rightarrow P = \dfrac{2,25,000}{26}\\[1em] \Rightarrow P = 8,653.85$

Hence, the principal amount = ₹ 8,653.85.