Question

The ages of Leena and Heena are in the ratio 7:5. Ten years hence, the ratio of their ages will be 9:7. Find the their present ages(solution with statement).

Answer 1

The ratio of the present ages of Leena and Heena = 7:5
Let the age of Leena be 7x years and Heena be 5x years
Ten years later their ages will be 7x +10 years and 5x + 10 years
but the ratio of their ages after ten years is given as 9:7
let their ages be 9x and 7x
∴9x + 7x = 7x + 10 + 5x + 10  
⇒9x = -7x + 7x + 10 + 5x + 10
⇒9x -5x = 10 + 10
⇒4x = 20
⇒x = 20/4 = 5
∴The age of Leena = 7x = 7* 5 = 35 years
And Heena`s age = 5x = 5* 5 = 25 years.

Answer 2

Answer:

The Present ages are -

• Leena = 35 years
• Heena = 25 years

Step-by-step explanation:

Given :

Ages of Leena and Heena are in Ratio = 7 : 5

Ratio after 10 Years = 9 : 7

To Find :

Their present Ages

Solution :

Let the present Ages be -

• Leena as 7x
• Heena as 5x

$\rule{300}{1.5}$

➡ (7x + 10)/(5x + 10) = 9/7

➡ 7(7x + 10) = 9(5x + 10)

➡ 49x + 70 = 45x + 90

➡ 49x - 45x = 90 - 70

➡ 4x = 20

➡ x = 20/4

➡ x = 5

$\rule{300}{1.5}$

Heena's age =

➡ 5 × 5

➡ 25

$\rule{300}{1.5}$

Leena's age =

➡ 7 × 5

➡ 35

$\therefore$ The Present ages are -

• Leena = 35 years
• Heena = 25 years