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प्रश्न
Divide Rs. 28,730 between A and B so that when their shares are lent out at 10% compound interest compounded per year, the amount that A receives in 3 years is the same as what B receives in 5 years.
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उत्तर
Let share of A = Rs. y
share of B = Rs (28,730 - y)
rate of interest = 10%
According to question,
Amount of A in 3 years = Amount of B in 5 years
⇒ `y( 1 + 10/100 )^3 = ( 28,730 - y)( 1 + 10/100 )^5`
⇒ `y = ( 28,730 - y )( 1 + 10/100)^2`
⇒ `y = ( 28,730 - y )( 121/100)`
⇒ 100y = 121(28,730 - y)
⇒ 100y + 121y = 121 × 28,730
⇒ 221y = 121 × 28,730
⇒ y = `[ 121 xx 28,730]/[221]` = Rs. 15,730
Therefore, share of A = Rs. 15,730
Share of B = Rs. 28,730 - Rs. 15,730 = Rs. 13,000
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