Question

the age of mother before 2 years was 8 times the age of a Daughter after one year mother's age will be 5 times a daughters age after how many years from now the mother's age will become three times the daughters age​

Answer 1

At Present:

• Mother = m
• Daughter = d

Before 2 years,

• Mothers age = m - 2
• Daughters age = d - 2

After 1 year,

• Mothers age = m + 1
• Daughters age = d + 1

According to the question,

(m - 2) = 8(d - 2)

⇒ m - 2 = 8d - 16

⇒ 8d - m = 16 - 2

⇒ 8d - m = 14   ⟶ (Equation 1)

Also,

m + 1 = 5(d + 1)

⇒ m + 1 = 5d + 5

⇒ m - 5d = 4

⇒ -5d + m = 4   ⟶ (Equation 2)

Adding equations 1 and 2,

            8d - m = 14

(+)       - 5d + m = 4

             3d = 18

⇒ d = 18÷3

⇒ d = 6 years

Substitute value of d in equation 1

m = 8d - 14

⇒ m = 8(6) - 14

⇒ m = 48 - 14

⇒ m = 34 years

Therefore

Mothers age = 34 years

Daughters age = 6 years

Their ages will become 3 times after 8 years

Verification:

3(6 + 8) = 34 + 8

→ 3 × 14 = 42

→ 42 = 42