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5 kg of sugar and 3 kg of tea leaves together cost ₹1050, while 3 kg of sugar and 2 kg of tea leaves cost ₹680. Find the cost of 1 kg of tea leaves (in ₹).

Class 10Pair of Linear Equations in Two VariablesAlgebra — Systems of Equations
  • A₹60
  • B₹310
  • C₹210
  • D₹250

Step-by-Step Solution

Let sugar cost and tea leaves per kg: and . Multiply by 2 and 3: and . Subtract: , then → . Check: ✓. ₹60 is the price of sugar, not tea; ₹310 is the difference 1050 − 680 − 60 mishandled.
Answer: D) ₹250

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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