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A steamer covers 36 km downstream in 2 hours, while the return trip of 36 km against the current takes 3 hours. Taking as the speed of the steamer in still water and as the speed of the current, find (in km/h).

Class 10Pair of Linear Equations in Two VariablesAlgebra — Systems of Equations
  • A15
  • B6
  • C3
  • D2.5

Step-by-Step Solution

Downstream speed = 36/2 = 18 and upstream speed = 36/3 = 12, so and . Subtract: → (and ). Check: h ✓ and h ✓. Choosing 15 answers with when the question asked for ; 6 is the difference 18 − 12 before halving it.
Answer: C) 3

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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