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The denominator of a fraction is 4 more than its numerator. If 3 is added to both the numerator and the denominator, the fraction becomes 4/5. Find the original fraction.

Class 10Pair of Linear Equations in Two VariablesAlgebra — Systems of Equations
  • A13/17
  • B9/13
  • C17/13
  • D5/9

Step-by-Step Solution

Let the fraction be . Then and → . Substituting → . Check: 16/20 = 4/5 ✓. 17/13 is the same numbers written upside down; 9/13 also has a denominator 4 more than the numerator but gives 12/16 = 3/4, not 4/5.
Answer: A) 13/17

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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