Question

The present ages of Vijay and Gautam are in the ratio 2 : 3. Five years hence, their ages will be in the ratio 3 : 4.Fins their present ages (You can assume the ages of Vijay and Gautam as 2x 3x, respectively.)

Answer 1

Answer:

10 yrs and 15 yrs respectively

Answer 2

Step-by-step explanation:

The ratio of present ages of Vijay and Gautam is 2 : 3

Let the present age of Vijay = 2x

And, present age of Gautam = 3x

Five years hence (later):-

Age of Vijay = 2x + 5

Age of Gautam = 3x + 5

Given, Five years hence, their ages will be in the ratio 3 : 4.

$\sf\dashrightarrow 2x + 5 : 3x + 5 = 3 : 4$

$\sf \dashrightarrow \dfrac{2x + 5}{3x + 5} = \dfrac{3}{4}$

$\sf \underline{By \: cross \: multiplication:-}$

$\sf \dashrightarrow 4(2x + 5) = 3(3x + 5)$

$\sf \dashrightarrow 8x + 20 = 9x + 15$

$\sf \dashrightarrow9x - 8x = 20 - 15$

$\sf \dashrightarrow x = 5$

Present age of Vijay = 2x = 2 × 5 = 10

Present age of Gautam = 3x = 3 × 5 = 15

Therefore:-

⇝ Present age of Vijay = 10 years

⇝ Present age of Gautam = 15 years