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Four years from now, Harish will be twice as old as his daughter. Four years ago, he was four times as old as she was. Taking as Harish's present age and as his daughter's, which pair of equations models the situation?

Class 10Pair of Linear Equations in Two VariablesAlgebra — Systems of Equations
  • A and
  • B and
  • C and
  • D and

Step-by-Step Solution

In four years: → . Four years ago: → . The sign of the second constant is where most slips happen: −4 + 16 = +12 must move across as −12. Options 3 and 4 reverse who is older or lose the minus signs. (Solving: — check ✓ and ✓.)
Answer: B) and

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 = age of A, = 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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