Question

A sum of Rs. 44200 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 cent per annum compound interest, they will receive equal amounts on reaching 16 years of age.
(i) What is the share of each out of Rs. 44,200?
(ii) What will each receive when 16 years old?

Answer 1

(i) Let share of Jhon = Rs y

Share of Smith = Rs (44,200 - y)

Rate of interest = 10%

According to question

Amount of Jhon in 4 years = Amount of Smith in 2 years

$$\Rightarrow y \left(1 + \dfrac{10} {100} \right)^{4} - \left(44,200 - y \right) \left(1 + \dfrac{10} {100} \right)^{2}$$

$$\Rightarrow y \left(1 + \dfrac{10} {100} \right)^{2} = \left(44,200 - y \right)$$

$$\Rightarrow y \left( \dfrac{11} {10} \right)^{2} = \left(44,200 - y \right)$$

$$\Rightarrow 121y = 100 \left(44,200 - y \right)$$

$$\Rightarrow 121y = 100 \times 44,200 - 100y$$

$$\Rightarrow 121y + 100y = 100 \times 44,200 $$

$$\Rightarrow 221y = 100 \times 44,200 $$

$$\Rightarrow y = \dfrac{100 \times 44,200} {221} = Rs 20,000$$

$$\therefore$$ Share of John = Rs 20,000

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

= Rs 24,200

(ii) Amount that each will receive

$$= 20,000 \left(1 + \dfrac{10} {100} \right)^{4} $$

$$= 20,000 \left( \dfrac{11} {10} \right)^{4} $$

= Rs 29,282