Question

The ages of Rahul and laxmi are in the ratio5:7.four years later, the sum of their ages will be 56 years. What are their present ages?

Answer 1

$\underline{\huge\mathbb{GIVEN:-}}$

❆ The ages of Rahul and Laxmi are in the ratio of 5 : 7.

❆ Four years later, the sum of their ages will be 56 years.

$\huge\underline{\mathbb{TO\ FIND:-}}$

The present ages of Rahul and Laxmi.

$\huge\underline{\mathbb{SOLUTION:-}}$

Let the present age of Rahul be 5x and the present age of Laxmi be 7x.

4 years later,

☞ Age of Rahul will be 5x + 4

☞ Age of Laxmi will be 7x + 4

A/q,

(5x + 4) + (7x + 4) = 56

➱ 5x + 4 + 7x + 4 = 56

➱ 12x + 8 = 56

➱ 12x = 56 - 8

➱ 12x = 48

➱ x = 48/12

➱ x = 4

Now,

➥ The present age of Rahul = 5x = 5 × 4 = 20 years

➥ The present age of Laxmi = 7x = 7 × 4 = 28 years

Answer 2

Answer :

The present age of Rahul is 20 years and that of Laxmi is 28 years

Given :

• The age of Rahul and Laxmi are in ratio of 5:7
• 4 years later , the sum of their ages will be 56 years.

To Find :

• The present ages of Rahuland Laxmi

Solition :

Let us consider the age of Rahul be x and that of Laxmi be y

According to Question :

Firstly the age of Rahul and Laxmi are in ratio of 5:7 i.e.

⇒x:y = 5:7

⇒ x/y = 5/7

⇒ x = (5/7)y ............(1)

Secondly 4 years later , the sum of their ages will be 56 years i.e.

⇒(x + 4)+(y + 4) = 56

⇒ x + 4 + y + 4 = 56

⇒ x + y + 8 = 56

⇒ x + y = 56 - 8

⇒ x + y = 48..........(2)

Puttung the value of x from (1) in (2) :

⇒(5/7)y + y = 48

⇒ (5y + 7y)/7 = 48

⇒ 12y = 48×7

⇒ y = (48×7)/12

⇒ y = 4×7

⇒ y = 28

Now from (1) by putting the value of y we have

⇒x = (5/7)×28

⇒ x = 5×4

⇒ x = 20

Thus the present ages of Rahul and Laxmi are 20 and 28 years respectively.