Question

son's of age is half of mother's age before a 10 years. Mother's age is 3 times of son's. Then find the present age? ​

Answer 1

Answer:

Given :-

• Son's age is half of mother's age. Before 10 years ago mother's age is 3 times of son's age.

To Find :-

• What is their present ages.

Solution :-

Let, the present age of son be x years

And, the present age of mother's will be 2x years

Before 10 years,

Age of son will be x - 10 years

And, the age of mother's will be 2x - 10 years

According to the question,

⇒ 3(x - 10) = 2x - 10

⇒ 3x - 30 = 2x - 10

⇒ 3x - 2x = - 10 + 30

➠ x = 20

Hence, the required present age are,

✧ Present age of son = x = 20 years

✧ Present age of mother = 2x = 2 × 20 = 40 years

∴ The present age of son is 20 years and the present age of mother is 40 years .

Let's Verify :-

↦ 3(x - 10) = 2x - 10

↦ 3x - 30 = 2x - 10

Put x = 20 we get,

↦ 3(20) - 30 = 2(20) - 10

↦ 60 - 30 = 40 - 10

↦ 30 = 30

➦ LHS = RHS

Hence, Verified ✔

Answer 2

Given:

✰ Son's age is half of mother's age before 10 years.

✰ Mother's age is 3 times of son's age.

To find:

Their present ages.

Solution:

Let the present age of mother be x years

Now, we know that the age of son is half ( 1/2 ) the age of mother, so

The present age of son = 1/2 of x

• The present age of mother = x years

• The present age of son = 1/2 x years

Now, ten years before means ten years ago, so we will substract 10 from both their ages

Ten years before,

☯ The age of mother = ( x - 10 ) years

☯ The age of son = ( 1/2x - 10 ) years

Now, we know that the age of mother is 3 times the age of son, which means 3 multiplied by son's age, then

According to the problem,

➟ x - 10 = 3 ( 1/2x - 10 )

➟ x - 10 = 3 × ( 1/2x - 10 )

➟ x - 10 = 3/2x - 30

➟ 2 ( x - 10 ) = 3 - 30

Now, multiply 2 on both sides,

➟ 2x - 20 = 3x - 60

➟ - 20 + 60 = 3x - 2x

➟ x = 40

Therefore, the present age of mother = 40 years

Now, we know that the age of son is half ( 1/2 ) the age of mother, so

The present age of son = 1/2 × x

The present age of son = 1/2 × 40

The present age of son = 20 years

Therefore,

• The present age of mother = 40 years

• The present age of son = 20 years

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