Question

6. The ratio of ages of Monu and Sonu is 5 : 7. Four years later, the ratio of their ages will be 3 : 4. Find their
present ages.​

Answer 1

$\large{\underline{\rm{\blue{\bf{Given:-}}}}}$

Ratio of the ages of Monu and Sonu = 5:7

Ratio of their ages 4 years later = 3:4

$\large{\underline{\rm{\blue{\bf{To \: Find:-}}}}}$

The present age of Monu.

The present age of Sonu.

$\large{\underline{\rm{\blue{\bf{Solution:-}}}}}$

Let us consider their present ages to be 5x and 7x respectively.

Then, after 4 years their ages would be,

Age of Monu after 4 years = $\sf 5x+4$

Age of Sonu after 4 years = $\sf 7x+4$

According to the question,

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

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

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

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

$\implies \sf 4=x$

Therefore,

Present age of Monu = 5x

$\implies \sf 5 \times 4=20 \: years$

Present age of Sonu = 7x

$\implies \sf 7 \times 7=28 \: years$

Therefore, the present age of Monu is 20 and Sonu is 28