A mother is at present three times as old as her son. Twelve years from now she will be twice as old as he is. What is the mother's present age (in years)?

Class 10Pair of Linear Equations in Two VariablesAlgebra — Systems of Equations

Step-by-Step Solution

Let the son be

s

and the mother

m

. Then

m = 3 s

and

m + 12 = 2 (s + 12)

, so

3 s + 12 = 2 s + 24

→

s = 12

and

m = 36

. Check: in 12 years they are 48 and 24, and

48 = 2 \times 24

✓. Answering 12 gives the son'

s

present age, and 48 gives the mother'

s

age twelve years from now rather than now.

Answer: D) 36

Key idea: Word problems and translation

Most Class 10 questions on this topic are word problems. The skill is in TRANSLATION:

1. Identify the two unknowns; assign variables (e.g., let

x

= age of A,

y

= age of B).
2. Write two equations from the two given pieces of information.
3. Solve by your preferred method.

**Common types**:
- **Age problems**: 'Father is twice as old as son. Five years ago father was three times. Find ages.'
- **Number problems**: 'A two-digit number plus its reverse is 99...'
- **Distance/time/speed**: 'Boat in still water speeds, downstream/upstream rates...'
- **Cost problems**: 'Cost of pencils and pens.'
- **Fraction problems**: 'A fraction becomes 1/2 when 1 is added to numerator and 2 is subtracted from denominator...'

Always CHECK by substituting solution back into the original word problem (not just the equations).

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