The ratio of present ages of Rehana and her mother is 2 : 7. After 2 y

1.	The ratio of present ages of Rehana and her mother is 2 : 7. After 2 years, the ratio of their ages will be 1 : 3.What is Rehana’s present age ?
Answer» The ratio of present ages of Rehana and her mother is 2 : 7 Let the common multiple be x. ∴ Present age of Rehana = 2x years and Present age of Rehana’s mother = 7x years After 2 years, Rehana’s age = (2x + 2) years Age of Rehana’s mother = (7x + 2) years According to the given condition, After 2 years, the ratio of their ages will be 1 : 3 ∴ \(\frac{2x\,+ \,2}{7x\, + \,2}\) = \(\frac{1}{3}\) ∴ 3(2x + 2) = 1(7x + 2) ∴ 6x + 6 = 7x + 2 ∴ 6 – 2 = 7x – 6x ∴ 4 = x ∴ x = 4 ∴ Rehana’s present age = 2x = 2 x 4 = 8 years ∴ Rehana’s present age is 8 years.

The ratio of present ages of Rehana and her mother is 2 : 7. After 2 years, the ratio of their ages will be 1 : 3.What is Rehana’s present age ?

Answer»

The ratio of present ages of Rehana and her mother is 2 : 7

Let the common multiple be x.

∴ Present age of Rehana = 2x years and Present age of Rehana’s mother = 7x years

After 2 years,

Rehana’s age = (2x + 2) years

Age of Rehana’s mother = (7x + 2) years

According to the given condition,

After 2 years, the ratio of their ages will be 1 : 3

∴ \(\frac{2x\,+ \,2}{7x\, + \,2}\) = \(\frac{1}{3}\)

∴ 3(2x + 2) = 1(7x + 2)

∴ 6x + 6 = 7x + 2

∴ 6 – 2 = 7x – 6x

∴ 4 = x

∴ x = 4

∴ Rehana’s present age = 2x = 2 x 4 = 8 years

∴ Rehana’s present age is 8 years.