Question

Five years ago, mother was three times older than daughter. Ten years later, mother will be twice as old as daughter. How old are daughter and mother now?

• A. (25,55)
• B. (20,50)
• C. (25,50)
• D. (20,55)

Hint:

Age problems are solved efficiently by assigning variables and forming linear equations.

Answer 1

The Correct Option is B

Step 1: Use first condition.
Five years ago: \[ M-5=3(D-5) \] \[ M=3D-10 \]

Step 2: Use second condition.
Ten years later: \[ M+10=2(D+10) \] \[ M=2D+10 \]

Step 3: Solve equations.
\[ 3D-10=2D+10 \] \[ D=20 \] Substituting: \[ M=2(20)+10=50 \]

Step 4: Answer.
\[ {(20,50)} \] Hence option (B) is correct.