Question

Q17. The ages of A and B are in the ratio 2:3. Six years ago, their ages were in the ratio 3:5. Find their present ages.​

Answer 1

Let present age of A = 2x

Let present age of B = 3x

Age of A 6 years ago = 3y

Age of B 6 years ago = 5y

2x - 6 = 3y. equation 1

3x - 6 = 5y. equation 2

Multiply eq 1 with 3 and eq 2 with 2.

6x - 18 = 9y

- 6x - 12 = 10y

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0 - 6 = -y

Therefore, y = 6.

Since, 2x - 6 = 3y,

2x - 6 = 18

2x = 24

x = 12.

Present age of A = 2x = 24 years

Present age of B = 3x = 36 years

Answer 2

★ Given :

• The ages of A and B are in the ratio 2:3.
• Six years ago, their ages were in the ratio 3:5.

★ To Find :

• Present age ?

★ Solution :

Let the sum of the ages of A = 2x

Let the sum of the ages of B = 3x

Then, After 6 ago, their ages are in the ratio 3:5

According to the question :-

∴ 2x - 6 / 3x - 6 = 3 / 5

Now, we will cross multiply.

↦ 5 ( 2x - 6 ) = 3 ( 3x - 6 )

↦ 10x - 30 = 9x - 18

↦ x = - 18 + 30

↦ x = 12

Present age of A = 2x = 2 × 12 = 24

Present age of B = 3x = 3 × 12 = 36

■ Hence, The present age of A and B is 24 years and 36 years.