Mother is 25 years older than her son. Find son’s age, if after 8 years ratio of son’s age to mother’s age will be 4/9 .

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Mother is 25 years older than her son. Find son’s age, if after 8 years ratio of son’s age to mother’s age will be 4/9 .

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Let the son’s present age be x years.

∴ Mother’s present age = (x + 25) years

After 8 years,

Son’s age = (x + 8) years

Mother’s age = (x + 25 + 8) = (x + 33) years .

Since, the ratio of the son’s age to mother’s age after 8 years is 4/9.

$\cfrac{x+8}{x+33} =\cfrac{4}{9}$

∴ 9 (x + 8) = 4 (x + 33)

∴ 9x + 72 = 4x + 132

∴ 9x – 4x = 132 – 72

∴ 5x = 60

∴ x = $\cfrac{60}{5}$

∴ x = 12

∴ Son’s present age is 12 years.

+1 vote
by (9.7k points)
Let the son’s present age be x years.

∴ Mother’s present age = (x + 25) years

After 8 years,

Son’s age = (x + 8) years

Mother’s age = (x + 25 + 8) = (x + 33) years

Since, the ratio of the son’s age to mother’s age after 8 years is 4/9

∴ (x + 8/x + 33) = 4/9

∴ 9 (x + 8) = 4 (x + 33)

∴ 9x + 72 = 4x + 132

∴ 9x – 4x = 132 – 72

∴ 5x = 60

∴ x = 12

∴ Son’s present age is 12 years.