Question

In 2014, the square of Chetan's age was half of Chetan's
mother's age. If present age of Chetan's mother is five times
the present age of Chetan (in 2017), then the age of Chetan
in 2020 will be
2014 में, चेतन की आयु का वर्ग चेतन की माँ की आयु का आधा था, यदि
चेतन की माँ की वर्तमान आयु चेतन की वर्तमान आयु (2017 में) की पाँच गुनी
है, तब 2020 में चेतन की आयु क्या होगी?
9 years
9 वर्ष
5 years
5 वर्ष
7 years
7 वर्ष
10 years
10 वर्ष​

Answer 1

Given:

In 2014, the square of Chetan's age was half of Chetan's  mother's age

In 2017, the present age of Chetan's mother is five times  the present age of Chetan

To find:

The age of Chetan  in 2020

Solution:

Let's assume,

"x" → represents the present age of Chetan

"y" → represents the present age of Chetan's mother

In 2017 (present year):

The equation giving the relation between Chetan and his mother's age in the present year is-

y = 5x ...... (i)

In 2014 i.e., 3 years ago:

Chetan's age was = (x - 3) years

Chetan's mother's age was = (y - 3) years

The equation giving the relation between Chetan and his mother's age 3 years ago in 2014 was-

$\bold{(x - 3)^2 = \frac{1}{2} (y - 3)}$

substituting the value of y from (i)

$\implies (x - 3)^2 = \frac{1}{2} (5x - 3)$

$\implies 2x^2 - 12x + 18 = 5x - 3$

$\implies 2x^2 - 17x + 21 = 0$

$\implies 2x^2 - 14x - 3x + 21 = 0$

$\implies 2x(x - 7)- 3(x - 7) = 0$

$\implies (x - 7)(2x -3) = 0$

$\implies x = 7 \:or \: x = \frac{3}{2}$

(the value of x = $\frac{3}{2}$ = 1.5 years is not possible because 1.5 years before 2017 will not be 2014 i.e., Chetan will not be born in the year 2014)

$\implies \bold{x = 7}$ .... (ii)

In 2020 i.e., 3 years later:

Chetan's age after 3 years will be = $x+ 3$

By substituting the value of x from (ii), we get

Chetan's age in 2020 = $7 + 3 = \bold{10 \:years}$

Thus, the age of Chetan in 2020 will be option (4):- 10 years.

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