Question

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.

Answer 1

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