Question

The present age of Sumit's mother is four times the present age of Sumit. After
5 years, the sum of their ages will be
60 years. Find their present ages.​

Answer 1

Given :

• Present age of Sumit's mother is four times the present age of Sumit.
• After 5 years, the sum of their ages will be 60 years.

To Find :

• Present Age of Sumit and his mother .

Solution :

$\longmapsto\tt{Let\:the\:age\:of\:Sumit\:be=x}$

As Given that present age of Sumit's mother is four times the present age of Sumit. So ,

$\longmapsto\tt{Present\:Age\:of\:Mother=4x}$

After 5 years :

$\longmapsto\tt{Age\:of\:Sumit=x+5}$

$\longmapsto\tt{Age\:of\:Mother=4x+5}$

A.T.Q :

$\longmapsto\tt{x+5+4x+5=60}$

$\longmapsto\tt{5x+10=60}$

$\longmapsto\tt{5x=60-10}$

$\longmapsto\tt{5x=50}$

$\longmapsto\tt{x=\cancel\dfrac{50}{5}}$

$\longmapsto\tt\bf{x=10}$

Value of x is 10 .

Therefore :

$\longmapsto\tt{Present\:Age\:of\:Sumit=x}$

$\longmapsto\tt\bf{10\:yrs}$

$\longmapsto\tt{Present\:Age\:of\:Mother=4(10)}$

$\longmapsto\tt\bf{40\:yrs}$

Answer 2

Given :-

The  present age of Sumit's mother is four times the present age of Sumit. After  5 years, the sum of their ages will be  60 years.

To Find :-

Present ages

Solution :-

Let the age of Sumit be y and Sumit's mother age be 4y

After 5 years

(y + 5) + (4y + 5) = 60

y + 5 + 4y + 5 = 60

(y + 4y) + (5 + 5) = 60

5y + 10 = 60

5y = 60 - 10

5y = 50

y = 50/5

y = 10

So,

Age of Sumit = 10 years

Age of Sumit's mother = 4(10) = 40 years