Question

A son’s present age is half the present age of his mother. Ten years ago, the mother was thrice as old as her son. What are their present ages?

Answer 1

✬ Son's age = 20 Years ✬

✬ Mother's age = 40 Years ✬

Given:

• Son's present age is half of his mother's present age.
• Ten years ago mother was thrice as old as her son.

To Find:

• What are the present ages of both ?

Solution: Let son age be x years and mother age be y years. Therefore

➟ Son's present age = Half of y

➟ x = y/2

➟ 2x = y.....(1)

[ Now, 10 years ago their ages was ]

• Son's age = (x – 10) years
• Mother's age = (y – 10) years

A/q

• Ten years ago mother was thrice as old as her son.

$\implies{\rm }$ (y – 10) = 3(x – 10)

$\implies{\rm }$ 2x – 10 = 3x – 30

$\implies{\rm }$ 2x – 3x = – 30 + 10

$\implies{\rm }$ – x = – 20

$\implies{\rm }$ x = 20

So, Present ages of

➙ Son is x = 20 years

➙ Mother is y = 2x = 2(20) = 40 years

Answer 2

GIVEN:

• Present age of the son is half the the present age of his mother.
• Ten years ago, the mother was thrice as old as her son.

TO FIND:

• What is the present age of son and mother ?

SOLUTION:

Let the present age of son be 'x' years and the present age of mother be 'y' years

CASE:-1)

❐ Present age of the son is half the the present age of his mother.

According to question:-

➸ y = 2x....❶

CASE:- 2)

❐ Ten years ago, the mother was thrice as old as her son.

According to question:-

• Mother's age = (y –10) years
• Son's age = (x –10) years

➸ y–10 = 3(x –10)

➸ y –10 = 3x –30

➸ y –3x = –30 + 10

➸ y –3x = –20

Put the value of 'y' from equation 1)

➸ 2x –3x = –20

➸ –x = –20

❮ x = 20 ❯

Put the value of 'x' in equation 1)

➸ y = 2 $\times$ 20

❮ y = 40 ❯

❝ Hence, the present ages of mother and son are 40 years and 20 years respectively. ❞

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