The difference in simple interest on a sum of money invested at 4% per annum for five years and for three years is ₹784. Find the simple interest (in ₹) on the same sum invested at the same rate of interest for eight years.
3136
Let the principal be \(P\) and the rate be 4% per annum.
Simple interest for \(n\) years is directly proportional to \(n\), since \(SI = \frac{P \times R \times n}{100}\).
So the difference between SI for 5 years and SI for 3 years equals the SI for \((5-3)=2\) years.
Given this difference is ₹784, so SI for 2 years \(= 784\), hence SI for 1 year \(= \frac{784}{2} = 392\).
SI for 8 years \(= 392 \times 8 = 3136\).
Hence, the simple interest for eight years is ₹3136.
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A certain sum amounts to Rs. 81840 in 3 years and to Rs. 92400 in 5 years at x% p.a. under simple interest. If the rate of interest is becomes (x + 2)%, then in how many years will the same sum double itself?
