Question

A principal of ₹4000 amounts to ₹5000 in 8 years at a certain rate of interest. In what time will ₹1600 amount to ₹2400 at the same rate?

Answer 1

Principal (P) = ₹4000; Amount = ₹5000,
hence, Interest(I) = ₹5000 - ₹4000 = ₹1000
Let the Rate be (R)
Time (T) = 8 years

I = $\frac{PTR}{100}$

1000 = $\frac{4000\times 8\times R}{100}$

R = $\frac{25}{8}$ %(1 Mark)

In the second case, Given: P = ₹1600 and Amount = ₹2400 , Hence, Interest(I) = ₹2400 - ₹1600 = ₹800( 1 Mark)

Let the time be n and rate of interest = $\frac{25}{8}$ %

800 = $\frac{1600\times 25\times n}{100\times 8}$

n = $\frac{800\times 8\times 100}{1600\times 25}$

n = 16 years (2 Marks)