Question

Present agesof rani and raju are in the ratio of 4:5 eight years from now the ratio of their ages willbe 5:6 find their present ages

Answer 1

$\mathfrak{\large{\underline{\underline{Answer :-}}}}$

Rani is 32 years old and Raju is 40 years old.

$\mathfrak{\large{\underline{\underline{Explanation :-}}}}$

Given :

Present ages of Rani and Raju = 4 : 5

Eight years from now the Ages = 5 : 6

To Find :

The Present ages

Solution :

Consider the Present ages as :

Rani = 4x

Raju = 5x

★ $\boxed{\sf{\frac{4x + 8}{5x + 8} = \frac{5}{6}}}$

$\sf{\implies} \: \dfrac{4x + 8}{5x + 8} = \dfrac{5}{6}$

$\sf{\implies} \: 6(4x + 8) = 5(5x + 8)$

$\sf{\implies} \: 24x + 48 = 25x + 40$

$\sf{\implies} \: 25x - 24x = 48 - 40$

$\sf{\implies} \: x = 8$

$\rule{300}{1.5}$

★ Value of 4x

$\sf{\implies} \: 4 \times 8$

$\sf{\implies} \: 32$

★ Value of 5x

$\sf{\implies} \: 5 \times 8$

$\sf{\implies} \: 40$

Rani = 32 years

Raju = 40 years

$\therefore$ Rani is 32 years old and Raju is 40 years old.

Answer 2

Answer -

Let the Ages after 8 years be 5x and 6x

==> (5x - 8)/(6x - 8) = 4/5

==> 5(5x - 8) = 4(6x - 8)

==> 25x - 40 = 24x - 32

==> 25x - 24x = -32 + 40

==> x = 8

Rani =

==> 4 × 8

==> 32

Raju =

==> 5 × 8

==> 40

Rani = 32 years

Raju = 40 years