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A cricket coach buys 7 bats and 6 balls for ₹3800. Later he buys 3 bats and 5 balls for ₹1750. Taking the cost of one bat as ₹ and one ball as ₹, the correct pair of equations is:

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

Step-by-Step Solution

Cost = (number of bats)(price of a bat) + (number of balls)(price of a ball), matched to the correct total. Option 2 swaps the roles of bat and ball, option 3 swaps the two totals, and option 4 lumps both purchases into a single equation — one equation in two unknowns can never pin down both prices. (Solving gives )
Answer: A) 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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