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A shop's price list says '3 pens and 4 notebooks cost ₹220'. A second, older list says '6 pens and 8 notebooks cost ₹k'. For which value of k do the two lists agree with each other instead of contradicting?

Class 10Pair of Linear Equations in Two VariablesAlgebra — Systems of Equations
  • A₹220
  • B₹110
  • C₹880
  • D₹440

Step-by-Step Solution

The second list doubles both quantities, so a₁/a₂ = 3/6 = 1/2 and b₁/b₂ = 4/8 = 1/2. The lists agree (coincident lines, infinitely many price pairs) only when 220/k = 1/2 as well, giving k = 440. For any other k the ratios give a₁/a₂ = b₁/b₂ ≠ c₁/c₂ — parallel lines and contradictory data. ₹110 comes from inverting the ratio and halving instead of doubling.
Answer: D) ₹440

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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