Question

The ages of Rohith and Hima are in the ratio 5:7. Four years later, their ages will be in the ratio 3:4. Find their ages​

Answer 1

Answer:-

Given:-

Ratio of present ages of Rohith and Hima = 5 : 7.

Let, their ages be 5x , 7x.

Also given that,

The ratio of their ages becomes 3 : 4 after 4 years.

According to the question,

$\implies \sf \: \frac{5x + 4}{7x + 4} = \frac{3}{4} \\ \\ \\ \implies \sf \:4(5x + 4) = 3(7x + 4) \\ \\ \\ \implies \sf \:20x + 16 = 21x + 12 \\ \\ \\ \implies \sf \:16 - 12 = 21x - 20x \\ \\ \\ \implies \boxed{ \sf \:4 = x}$

∴

• Rohith's present age = 5x = 5(4) = 20 years

• Hima's present age = 7x = 7(4) = 28 years.

Answer 2

Answer:

Given :-

Ages of Rohith and Hima are in the ratio 5:7. Four years later, their ages will be in the ratio 3:4.

To Find :-

Ages

Solution :-

Let their present ages be 5x and 7x respectively.

$\sf \bigg \{ \dfrac{5x + 4}{7 x + 4} \bigg \} = \dfrac{3}{4}$

By cross multiplication

$\sf \: 4(5x + 4) = 3(7x + 4)$

$\sf \: 20x + 16 = 21x + 12$

$\sf \: 20x - 21x = 12 - 16$

$\sf \: - x = - 4$

$\sf \: x = 4$

Present age of Rohit = 5x = 20 years

Present age of Hima = 7x = 28 years