Question

an amount of money appreciates to Rs7000 after 4 years and to Rs 10000 after 8 years at a certain compound interest compounded annually. The initial amount of money was a) Rs 4,700 b) Rs4,900 c) Rs4,100 d) Rs4,300 Kindly show me some way of solving this question in the least amount of time, like in olympiad

Answer 1

Let the amount be P
As we know, A = P(1 + R/100)^t
initially, 7000 = P(1+R/100)^4________(1)
The key point to note here is, after 4 years, Rs 7000 will be the principal and the  amount after further 4 years will be Rs 10000
so,
10000 = 7000(1 +R/100)^4
⇒(1 +R/100)^4 = 10/7 
putting this value in equation (1),
7000 = P×10/7
⇒P = Rs 4900
By applying small logic you can make easier your problems.