Question

A sum of Rs 44,200 is divided between John and Smith, 12 years and 14 years old respectively, in such a way that if their portions be invested at 10% per annum compound interest, they will receive equal amounts on reaching 16 years of age.
(i) What is the share of each out of Rs44,200 ?
(ii) What will each receive, when 16years old ?

Answer 1

(i) Let share of John = Rs y
share of Smith = Rs (44,200 - y)
rate of interest= 10%

According to question,
Amount of John in 4 years = Amount of Smith in 2 years

⇒ `y( 1 + 10/100)^4 = ( 44,200 - y)( 1 + 10/100)^2`

⇒ `y( 1 + 10/100 )^2 = ( 44,200 - y)`

⇒ `y( 11/10 )^2 = ( 44,200 - y)`

⇒ `121y = 100( 44,200 - y)`

⇒ `121y = 100 xx 44,200 - 100y`

⇒ `121y + 100y = 100 xx 44,200`

⇒ `221y = 100 xx 44,200`

⇒ `y = 100 xx 44,200/221` = Rs. 20,000.

Therefore share of John =Rs. 20,000

Share of Smith = Rs. 44,200 - Rs. 20,000 = Rs. 24,200

(ii) Amount that each will receive

= `20,000( 1 + 10/100 )^4`

= `20,000(11/10)^4`

= Rs. 29,282