Question

Shikha and Riya are friends and their ages differ by $2$ years. Shikha's father Rajiv is twice as old as Shikha and Riya is twice as old as her sister Maya. The age of Rajiv and Maya differ by 40 years Then the age of Shikha and Riya respectively are _______

• A. $26$ years, $24$ years
• B. $27\frac{1}{3}$ years, $29\frac{1}{3}$ years
• C. $27$ years, $29$ years
• D. Both (A) and (B)

Answer 1

The correct option is D Both (A) and (B)

First case

let the age of Shikha$=x$ years
then Riya age$=x+2$ years
According to the question,
Shikha's father Rajiv age$=2x$
Maya age=$\frac{x+2}{2}$
Then $2x-\left(\frac{x+2}{2}\right)=40$
$4x-x-2=80$
$3x=82$
$x=27\frac{1}{3}$
Hence Shikha age is $27\frac{1}{3}years$ and Riya age is $27\frac{1}{3}+2=29\frac{1}{3}years$

Second case

LIet Shikha's age be $x$, then Riya age$=x-2$ years

According to the question,
Shikha's father Rajiv age$=2x$
Maya age=$\frac{x-2}{2}$
Then $2x-\left(\frac{x-2}{2}\right)=40$
$4x-x+2=80$
$3x=78$

$x=26$

Hence Shikha age is $26years$ and Riya age is $26-2=24years.$