Question

14
A person's present age is one-fifth of the age of
his mother. After 7 years, he will be one-third of
the age of his mother. How old is the mother at
present in years)?
(a) 35
(b) 40
(©) 45
(d) 50​

Answer 1

$\bf\underline{\huge{ANSWER}}$

$\rm Let,\\\\Present \ age \ of \ mother =x \ years\\\\Present \ age \ of \ the \ person = \dfrac{x}{5} \ years\\\\After \ 7 \ years ,\\\\Age \ of \ mother = (x+7) \ years\\\\Age \ of \ the \ person = \left ( \dfrac{x}{5}+7 \right) \ years$

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$\rm According \ to \ the \ question \ ,\\\\\longrightarrow \dfrac{x}{5}+7=\dfrac{x+7}{3}\\\\\longrightarrow \dfrac{x+35}{5}=\dfrac{x+7}{3}\\\\\longrightarrow 3(x+35)=5(x+7)\\\\\longrightarrow 3x+105=5x+35\\\\\longrightarrow 5x-3x=105-35\\\\\longrightarrow 2x=70\\\\\longrightarrow \bf\underline{x=35}$

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Present age of mother = 35 years

Answer 2

Given:

A person's present age is one-fifth of the age of

his mother. After 7 years, he will be one-third of

the age of his mother.

To find:

The present age of the mother.

Solution:

Let the present age of the person's mother be x years.

So,

the present age of the person

$= \frac{1}{5} \times \: x$

$= \frac{x}{5} \: years$

Now,

After 7 years, the age of the person's mother = (x + 7) years.

After 7 years, the age of the person =

$( \frac{x}{5} + 7) \: years$

Now,

according to the question,

After 7 years, the person's age will be one-third of

the age of his mother.

So,

$\frac{x}{5} + 7 = \frac{1}{3} (x + 7)$

On solving the above, we get,

$\frac{x}{3} - \frac{x}{5} = 7 - \frac{7}{3}$

Taking 15 and 3 as LCM on LHS and RHS respectively, we have,

$\frac{2x}{15} = \frac{14}{3}$

$x = \frac{14 \times 15}{3 \times 2}$

$x = 7 \times 5$

$x = 35 \: years$

Hence, the present age of the mother is (a) 35 years.