Question

The present age of shruti and swati is in ratio 4:5 eight years hebce the tmratio kf their agrd will be 5:6 find their pfesent agr

Answer 1

$\textbf{\underline{\underline{Answer :-}}}$

The present age of Shruti is 32 years and Swati is 40 years.

$\textbf{\underline{\underline{Explanation :-}}}$

Given :

Present age Ratio = 4:5

Ratio after 8 years = 5:6

To find :

Their present ages

Solution :

Consider the present age of Shruti as 4x

Consider the present age of Swati as 5x

$\star$ Equation :-

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

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

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

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

$\tt{\implies} - x = - 8$

$\tt{\implies}\cancel{ - } \: x = {\cancel{ - }} \: 8$

$\tt{\implies}x = 8$

Value of 4x

$\tt{\implies}$ 4 × x

$\tt{\implies}$ 4 × 8

$\tt{\implies}$ 32

Value of 5x

$\tt{\implies}$ 5 × x

$\tt{\implies}$ 5 × 8

$\tt{\implies}$ 40

$\therefore$The present age of Shruti is 32 years and Swati is 40 years.

$\textbf{\underline{\underline{Verification :-}}}$

$\tt{\implies} \dfrac{(4 \times 8) + 8}{(5 \times 5)+ 8} = \dfrac{5}{6}$

$\tt{\implies} \dfrac{32 + 8}{40 + 8} = \dfrac{5}{6}$

$\tt{\implies} \dfrac{40}{48} = \dfrac{5}{6}$

Reduce it

$\tt{\implies} \dfrac{5}{6} = \dfrac{5}{6}$

LHS = RHS

$\therefore$The present age of Shruti is 32 years and Swati is 40 years.