Question

the present ages of Akansha and Tripti are in the ratio 4:5. Eight years from now , their ages will be in the ratio 5:6 . Find their present ages.

Answer 1

Given, present ages of Akansha and Tripti are in the ratio 4 : 5

Let the constant be x

Let the present age of Akansha be 4x and Tripti by 5x

8 years from now, age of Akansha = 4x + 8 and age of Tripti = 5x + 8

8 years from now, the ratio of their ages will become 5 : 6


According to the question,

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

By cross multiplying,

➾ $6(4x\:+\:8)\:=\:5(5x\:+\:8)$

➾ $24x\:+48\:=\:25x\:+\:40$

➾ $24x\:-\:25x\:=\:40\:-\:48$

➾ $-x\:=\:-8$

➾ $x\:=\:8$


∴ Present age of Akansha ➾ 4x

➾ 4 × 8

➾ $\green{\boxed{\green{\boxed{\red{\textsf{32\:years}}}}}}$


∴ Present age of Tripti ➾ 5x

➾ 5 × 8

➾ $\green{\boxed{\green{\boxed{\red{\textsf{40\:years}}}}}}$

Answer 2

=> Consider the common constant as X

=> So, the AGES =

=> Akansha = 4X

=> Tripti = 5X

Corresponding fraction =

$\large = > \frac{4x}{5x}$

=> Eight years hence =

=> Akansha = 5

=> Tripti = 6

Corresponding fraction =

$\large = > \frac{5}{6}$

So, the equation =

$\large = > \frac{4x + 8}{5x + 8} = \frac{5}{6}$

=> Cross Multiply =

$\large= > 6(4x + 8) = 5(5x + 8)$


$\large= > 24x + 48 = 25x + 40$


$\large = > 24x - 25x = 40 - 48$


$\large= > - x = - 8$

$\large = > x = 8$

Akansha's age = 4X

=> 4 × 8

=> 32 years

Tripti's age = 5X

=> 5 × 8

=> 40 years

Therefore the present ages of Akansha and Tripti are 32 and 40 years respectively.