Question

the ages of rahul and laxmi are in the ratio of 4:5.after ten years hence the ratio of their age will be 9:10. find their present ages.​

Answer 1

☆ Given :

• Age of Rahul and Laxmi are in ratio 4 : 5
• After ten years hence, the ratio of their age will be in ratio 9 : 10

☆ To find :

• The present ages of Rahul and Laxmi.

☆ Solution :

Let the age of Rahul be 4x

And Age of Laxmi be 5x

Ten years hence,

Age of Rahul = 4x + 10

Age of Laxmi = 5x + 10

According to Question,

↣ 4x+10 : 5x+10 = 9 : 10

↣ 4x+10/5x+10 = 9/10

↣ 10(4x + 10) = 9(5x + 10)

[By cross multiplicatio]

↣ 40x + 100 = 45x + 90

↣ 40x - 45x = 90 - 100

↣ -5x = -10 [(-) & (-) got cancelled]

↣ 5x = 10

↣ x = 10/5

↣ x = 2

Therefore,

• Present age of Rahul (4x) = 4×2 = 8years
• Present age of Laxmi (5x) = 5×2 = 10years

Answer 2

Step-by-step explanation:

$\text{The ages of rahul and laxmi are in the ratio of 4:5}$

$\text{Let the their ages be x }$

$\sf \: Than$

$\sf \: Rahul's \: \: age = \: 4x$

$\sf \: Laxmi ' s \: \: age = 5x$

$\sf \: After \: \: ten \: \: years$

$\text{Rahul's age = 4x + 10}$

$\text{Laxmi 's age = 5x + 10}$

$\underline{ \sf \: According \: to \: the \: question}$

$\sf \: \frac{4x + 10}{5x + 10} = \frac{9}{10}$

$\text{We will cross multiply now}$

$\sf \: 10(4x \: + 10) = 9(5x + 10)$

$\sf \: 40x + 100 = 45x + 90$

We we change the digits their sigh will also change

$\sf \: 40x - 45x = 90 - 100$

$\sf \: - 5x = -10$

$x = \cancel\frac{10}{ 5}$

$x = 2$

Rahul's age = 4x = 4 X 2 = 8 years

Laxmi's age = 5x = 5 X 2 = 10 years