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A lending library charges a fixed fee for the first three days and an extra charge for every day after that. Meera paid ₹27 for a book she kept for 7 days, and Farida paid ₹21 for a book she kept for 5 days. Find the fixed fee (in ₹).

Class 10Pair of Linear Equations in Two VariablesAlgebra — Systems of Equations
  • A₹6
  • B₹15
  • C₹3
  • D₹12

Step-by-Step Solution

Let the fixed fee be and the extra daily charge . Meera has 7 − 3 = 4 extra days and Farida 5 − 3 = 2, so and . Subtract: → and . Check: ✓ and ✓. ₹3 is the per-extra-day charge; ₹6 comes from writing and , forgetting that the first three days are already inside the fixed fee.
Answer: B) ₹15

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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