Question

the age melat is five times older than the age of hana . in ten years time the ratio of the age of hana to melat is 5:9.find the present age of hana and melat?

Answer 1

Step-by-step explanation:

As per the question:

Given:

• Melat's age is 5 times as that of Hana.
• After 10 years, age of Hana to the age of Melat will be in the ratio of 5:9.

To find:

• Hana's and Melat's present ages.

Solution:

Let,

Hana's present age be = x

So, Melat's age will be = 5x

After 10 years,

Hana's age = x + 10

Melat's age = 5x + 10

By the problem,

$= > \: \frac{x + 10}{5x + 10} = \frac{5}{9}$

• [By cross multiplication]

=> 9(x + 10) = 5(5x + 10)

• [By multiplication]

=> 9x + 90 = 25x + 50

• [Shifting like terms to the same sides]

=> 25x - 9x = 90 - 50

• [On subtraction]

=> 16x = 40

• [Dividing both sides by 16]

$= > \: \frac{16x}{16} = \frac{40}{16}$

=> x = 2.5

Hence,

The present age of Hana is 2 years 6 months.

The present age of Melat 12 years 6 months.