The ages of sam and rahul …

Let the present ages of Hari and Harry be 5x years and 7x years respectively.
Four years from now
Age of Hari = (5x + 4) years
Age of Harry = (7x + 4) years
According to the question,
{tex}\frac{{5x + 4}}{{7x + 4}} = \frac{3}{4}{/tex}
{tex}\left( {\frac{{5x + 4}}{{7x + 4}}} \right) \times (7x + 4) = \frac{3}{4} \times (7x + 4){/tex} . . . . [ Multiplying both sides by 7x + 4, we get ]
∴ {tex}5x + 4 = \frac{{3(7x + 4)}}{4}{/tex}
 4(5x + 4) = 3(7x + 4)  . . . . [ Multiplying both sides by 4, we get ]
∴ 20x + 16 = 21x + 12
∴ 16 – 12 = 21x – 20x
∴ 4 = x
∴ x = 4
∴ 5x = 5 × 4 = 20
and 7x = 7 × 4 = 28  hence, their present ages are 20 years and 28 years respectively.
Verification
{tex}20:28 = \frac{{20}}{{28}} = \frac{{20 \div 4}}{{28 \div 4}} = \frac{5}{7} = 5:7{/tex}
20 + 4 = 24
28 + 4 = 32 
{tex}24:32 = \frac{{24}}{{32}} = \frac{{24 \div 8}}{{32 \div 8}} = \frac{3}{4} = 3:4{/tex} hence, the result is verified.