Question

Rohan's mother is $12$ years more than twice his age. After $8$ years, his mother’s age will be $20$ years less than thrice his age. Find Rohan's age and his mother’s age.

• A. $\text{16 and 48}$
• B. $\text{16 and 44}$
• C. $\text{12 and 36}$
• D. $\text{54 and 14}$

Answer 1

The correct option is B $\text{16 and 44}$

Let the age of rohan be $x$ years.
His mother's age is $(2x+12)$ years
After $8$ years Rohan age will be $x+8$ and his mother age be
$(2x+12+8)=2x+20$
So, According to the question,

So, $2x+20=3(x+8)-20$
Or $2x+20=3x+24-20$
Or $2x+20=3x+4$
Or $x=16$
So, Rohan age $=16$years
His mother’s age is $2\left(16\right)+12=32+12=44$ years.