Question
A deposits an amount x at 5% per annum simple interest
in a bank. His brother B deposits an amount y at 10% annual interest compounded annually. After 1 year, the interest received by B is twice the interest received by A. What is the value of y : x?Solution
For A, Principal = x; Rate = 5%; Time = 1 year Simple Interest = ( Principal Ă— Rate Ă— Time ) / 100 S.I = ( x Ă— 5 Ă— 1 ) / 100 S.I = x / 20Â Â Â Â ---- (1) For B, Principal = y; Rate = 10%; Time = 1 year = n Amount = Principal [ 1 + ( Rate / 100 ) ]n Amount = y [ 1 + ( 10 / 100 ) ]1 Amount = 11y / 10 Compound Interest = ( 11y / 10 ) - y C.I = y / 10Â Â ---- (2) We know that Interest ratio is 2x : y. So, 2 Ă— (x / 20) = y / 10 x / 10 = y / 10 x = y Hence, x: y = 1:1
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