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The sum of a two-digit number and the number obtained by reversing its digits is 110. If the digits differ by 2, and the tens digit is larger, find the original number.

Class 10Pair of Linear Equations in Two VariablesAlgebra — Systems of Equations
  • A64
  • B58
  • C70
  • D128

Step-by-Step Solution

Let tens = , units = → → . Also . Solving: . Original = 64.
Answer: A) 64

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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