- A16
- B9
- C7
- D8
Step-by-Step Solution
Let boat speed = . Downstream speed = , upstream = . Equal times for given distances: → → → → .
Answer: D) 8
A boat goes 30 km downstream in the same time it takes to go 18 km upstream. If the speed of the stream is 2 km/h, find the speed of the boat in still water (in km/h).
Class 10Pair of Linear Equations in Two VariablesAlgebra — Systems of Equations
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).
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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