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Question
Anuj and Rajesh each lent the same sum of money for 2 years at 8% simple interest and compound interest respectively. Rajesh received Rs. 64 more than Anuj. Find the money lent by each and interest received.
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Solution
Let the sum of money lent by both Rs. y
For Anuj
P = Rs.y ; rate = 8% and time = 2 years
∴ S.I. = `[ "P" xx "R" xx "T" ]/100 = [ y xx 8 xx 2 ]/100 = (4y)/25`
For Rajesh
P = Rs. y ; rate = 8% and time = 2 years
∴ C.I. = P`[(1 + r/100)^n - 1] = y[( 1 + 8/100)^2 - 1] = (104y)/(625)`
Given : C.I. - Rs. 64
⇒ `(104y)/(625) - (4y)/(25) = 64`
⇒ `(4y)/(625) = 64`
⇒ `y = [64 xx 625]/4` = Rs. 10,000
Interest received by Anuj = `[ 4 xx 10,000 ]/25` = Rs. 1600
Interest received by Rajesh = `[ 104 xx 10,000 ]/625` = Rs. 1664.
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