A person's present age is two - fifth of the age of his mother. After 8 years. he will be one half of the age of his mother . What is the present age of the mother?

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বাংলাদেশ ব্যাংক || সহকারী পরিচালক 28-10-2022 গণিত বয়স (Ages)

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Suppose, mother's age is x, hence person's age is $\frac{2 x}{5}$

After 8 years, mother's age will be x + 8 and person's age will be $\frac{2 x}{5} + 8 = \frac{2 x + 40}{5}$

According to question,

$x + 8 = \frac{2 x + 40}{5} \times 2$

$\Rightarrow x + 8 = \frac{4 x + 80}{5}$

$\Rightarrow 5 x + 40 = 4 x + 80$

$\Rightarrow 5 x - 4 x = 80 - 40$

$∴ x = 40$

Hence, mother's present age is 40

2 years ago

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Shuvra

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