Question

The ages of Mohan and Sohan are in the ratio 5 : 7 . If Mohan was 9 years older and Sohan 9 years younger , then their ages would be in the ratio 2 : 1 . Find their present ages .​

Answer 1

Answer:

Let x be the present age of mohan and sohan then present age of mohan is 5x and that of sohan is 7x.

According to 1st condition -

Mohan's age will be 5x+9

Sohan's age will be 7x−9

⇒5x+9:7x−9=2:1

⇒7x−95x+9=12

⇒(5x+9)=2(7x−9)

⇒5x+9=14x−18

⇒5x−14x=−18−9

⇒−9x=−27

⇒x=3

Present age of mohan is 5x=5×3=15

Present age of sohan is 7x=7×3=21

hence, solved.

Answer 2

ANSWER:

Given:

• Ratio of ages of Mohan and Sohan = 5 : 7
• If Mohan was 9 years older and Sohan 9 years younger , then ratio = 2 : 1

To Find:

• Their present ages.

Solution:

Let the present ages of Mohan and Sohan be 5x and 7x respectively.

Now,

We are given a condition that,

⇒ If Mohan was 9 years older and Sohan 9 years younger , then ratio = 2 : 1

This means,

⇒ (5x + 9) : (7x - 9) = 2 : 1

So,

⇒ (5x + 9) / (7x - 9) = 2 / 1

On cross-mutliplying,

⇒ 1 × (5x + 9) = 2 × (7x - 9)

⇒ 5x + 9 = 14x - 18

Transposing 18 to LHS and 5x to RHS,

⇒ 9 + 18 = 14x - 5x

⇒ 27 = 9x

⇒ 9x = 27

⇒ x = 27/9

⇒ x = 3

Hence, present ages of Mohan and Sohan:

• Mohan = 5x = 5 × 3 = 15
• Sohan = 7x = 7 × 3 = 21

Therefore, the present ages of Mohan and Sohan are 15 years and 21 years respectively.