(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