Question

The sum of ages of ajay and vijay is 55 years. 10 years ago the age of ajay is 4/3 times of age of vijay

Answer 1

${\underline{\underline{\huge{\mathfrak{\green{Answer:-}}}}}}$

Hey Mate!!

Let age of Vijay be x and age of Ajay be y.

According to the question,

x + y = 55

=> y = 55 - x .......(1)

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Vijay's age 10 years ago = x - 10

Ajay's age 10 years ago = y - 10

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According to question,

$\frac{4}{3} (x - 10) = y - 10 \\ = > \frac{4}{3} x - \frac{40}{3} = y - 10 \\ = > \frac{4}{3} x - y = \frac{40}{3} - 10 \\ = > \frac{4}{3} x - y = \frac{40 - 30}{3} \\ = > \frac{4}{3} x - y = \frac{10}{3} \: \: \: .....(2)$

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By substituting (1) in (2),

$\frac{4}{3} x - (55 - x) = \frac{10}{3} \\ = > \frac{4}{3} x - 55 + x = \frac{10}{3} \\ = > \frac{4}{3} x + x = \frac{10}{3} + 55 \\ = > \frac{4 + 3}{3} x = \frac{10 + 165}{3} \\ = > \frac{7}{3} x = \frac{175}{3} \\ = > x = \frac{175}{3} \times \frac{3}{7} \\ = > x = 25 \: years$

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Therefore,

Vijay's age = x = 25 years

Ajay's age = y = 55 - x = 30 years

Therefore, Vijay is 25 years old and Ajay is 30 years old.