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प्रश्न
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.
उत्तर
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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