Five years ago, Sanjana was thrice as old as Sanjay. Ten years later, Sanjana will be twice as old as Sanjay. The ages of Sanjay and Sanjana are respectively
A. 20
B. 30
C. 40
D. 50
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → A and D only
Let Sanjay’s present age be \(x\) years and Sanjana’s \(y\) years. Each condition gives one equation, and equating the two values of \(y\) gives \(x\).
The two conditions:
Five years ago: \(y-5=3(x-5)\), so \(y=3x-10\) (1)
Ten years later: \(y+10=2(x+10)\), so \(y=2x+10\) (2)
Equating (1) and (2):
\(3x-10=2x+10\)
\(x=20\), so Sanjay is 20 (A)
From (2): \(y=2(20)+10=50\), so Sanjana is 50 (D)