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Two taps running together fill a tank in 12 hours. If and are the hours each tap would take on its own, which equation correctly describes the situation?

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

Step-by-Step Solution

Add the WORK done per hour, not the times. In one hour the first tap fills of the tank and the second , and together they fill 1/12. So , which becomes the linear equation under . Adding the times as is the classic error — it would mean the taps take longer together than alone.
Answer: B)

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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