The ratio of present ages of Albert and Salim is 5 : 9. Five years hen

1.	The ratio of present ages of Albert and Salim is 5 : 9. Five years hence ratio of their ages will be 3 : 5. Find their present ages.
Answer» The ratio of present ages of Albert and Salim is 5 : 9 Let the common multiple be x. ∴ Present age of Albert = 5x years and Present age of Salim = 9x years After 5 years, Albert’s age = (5x + 5) years and Salim’s age = (9x + 5) years According to the given condition, Five years hence ratio of their ages will be 3 : 5 \(\frac{5x+5}{9x+5}\) = \(\frac{3}{5}\) ∴ 5(5x + 5) = 3(9x + 5) ∴ 25x + 25 = 27x + 15 ∴ 25 – 15 = 27 x – 25 x ∴ 10 = 2x ∴ x = 5 ∴ Present age of Albert = 5x = 5 x 5 = 25 years Present age of Salim = 9x = 9 x 5 = 45 years ∴ The present ages of Albert and Salim are 25 years and 45 years respectively.

The ratio of present ages of Albert and Salim is 5 : 9. Five years hence ratio of their ages will be 3 : 5. Find their present ages.

Answer»

The ratio of present ages of Albert and Salim is 5 : 9

Let the common multiple be x.

∴ Present age of Albert = 5x years and

Present age of Salim = 9x years

After 5 years,

Albert’s age = (5x + 5) years and

Salim’s age = (9x + 5) years

According to the given condition,

Five years hence ratio of their ages will be 3 : 5

\(\frac{5x+5}{9x+5}\) = \(\frac{3}{5}\)

∴ 5(5x + 5) = 3(9x + 5)

∴ 25x + 25 = 27x + 15

∴ 25 – 15 = 27 x – 25 x

∴ 10 = 2x

∴ x = 5

∴ Present age of Albert = 5x = 5 x 5 = 25 years

Present age of Salim = 9x = 9 x 5 = 45 years

∴ The present ages of Albert and Salim are 25 years

and 45 years respectively.