41. The present age of Mohan's mother is four times that of Mohan's ag

1.	41. The present age of Mohan's mother is four times that of Mohan's age. Mohan's age ten years from now will beone third of his mother's present age. What are their present ages?
Answer» 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 $\sf{y=<klux>4X</klux>}$ . . .(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.

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

Answer»

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.

The present ages of Mohan and his mother.

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

According to the question,

CASE - 1

$\sf{y=<klux>4X</klux>}$ . . .(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.