Question

In how much time will the simple interest on Rs 3,000 at the rate of 8% per annum be the same as simple interest on 4,000 at 12% per annum for 4 years?

Answer 1

Let the required number of years be x 

Simple Interest I = \(\frac{pnr}{100}\)

Principal P₁ = Rs 3000 

Rate of interest (r) = 8 % 

Time (n₁) = n₁ years 

Simple Interest I₁ = \(\frac{3000\,\times\,8\,\times\,n_1}{100}\)

= 240 n₁ 

Principal (P₂) = Rs 4000 

Rate of interest (r) = 12 % 

Time n₂ = 4 years 

Simple Interest I₂ = \(\frac{4000\times12\times4}{100}\)

I₂ = 1920 

If I₁ = I₂ 

240 n₁ = 1920 

n₁ = \(\frac{1920}{240}\)

= 8 

∴ The required time = 8 years