Question

13.The ages of A and B are in the ratio 7:9.Four years from now, their ages will be 4:5.Then the present age of A is *​

Answer 1

Required Answer :

Present age of A = 28 years

Given :

• Ratio of the ages of A and B = 7 : 9
• The ratio of their ages after 4 years = 4 : 5

To find :

• Present age of A

Solution :

Let,

• The present age of A = 7x
• The present age of B = 9x

Their ages after 4 years :

⇒ Age of A = 7x + 4 years

⇒ Age of B = 9x + 4 years

According to the question,

⇒ (Age of A)/(Age of B) = 4/5

⇒ (7x + 4)/(9x + 4) = 4/5

⇒ 5(7x + 4) = 4(9x + 4)

⇒ 35x + 20 = 36x + 16

⇒ 20 - 16 = 36x - 35x

⇒ 4 = 1x

⇒ x = 4

• The value of x = 4

Substituting the value of x in the present age of A :

⇒ Present age of A = 7x

⇒ Present age of A = 7(4)

⇒ Present age of A = 28 years

Answer 2

Given:

• The ages of A and B are in the ratio 7:9.Four years from now, their ages will be 4:5.

To Find:

• Present age of A

Solution:

• Let Present age of A = 7x
• Present age of B = 9x

Ages after 4 years,

• A's age = (7x + 4) years
• B's age = (9x + 4) years

According to Question,

→ (7x + 4)/(9x + 4) = 4/5

→ 5 (7x + 4) = 4 (9x + 4)

→ 35x + 20 = 36x + 16

→ 20 - 16 = 36x - 35x

→ x = 4

Now,

Present age of A = 7x = 28 years

Hence,

• Present age of A is 28 years.

━━━━━━━━━━━━━━━━━━━━━━━━