Question

41. The present age of Mohan's mother is four times that of Mohan's age. Mohan's age ten years from now will be
one third of his mother's present age. What are their present ages?
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Answer 1

Given :-

• The present age of Mohan's mother is four times that of Mohan's age.
• Mohan's age ten years from now will be  one third of his mother's present age.

To Find :-

The present ages of Mohan and his mother.

Solution :-

Let the present age of Mohan be x and the present age of Mohan's mother be y.

According to the question,

CASE - 1

$\sf{y=4x}$      . . .(i)

____________________

CASE - 2

$\sf{x+10=\dfrac{1}{3}\times (y+10) }$

Substituting value of y from (i) :-

$\longmapsto \sf{x+10=\dfrac{1}{3}\times (4x+10) }$

$\longmapsto \sf{3(x+10)=4x+10}$

$\longmapsto \sf{3x+30=4x+10}$

$\longmapsto \sf{30-10=4x-3x}$

$\longmapsto \sf{20=x}$

____________________

Therefore, the present age of Mohan = x = 20 years.

The present age of Mohan's mother = y = 4x = 4 × 20 = 80 years.

Answer 2

Given:

• The present of Mohan's mother age is four times of Mohan's age.

Let,

Mohan's age be x years

So, Mohan's mother age is (4x) years

According to the question,

• Mohan's age ten years from now will be one-third of his mother's present age.

So,

(x + 10) = 1/3 * (4x+10)

⇒ x + 10 = (4x+10)/3

⇒ 3 * (x + 10) = 4x+10

⇒ 3x + 30 = 4x + 10

⇒ 30 - 10 = 4x - 3x

⇒ 20 = x

So,

• The age of Mohan is x years = 20 years.

And

• Age of Mohan's mother age is 4x = 4 * 20 = 80 years