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Pair of Linear Equations in Two Variables
CH03 Question Bank
CBSE_CH03_QUESTION_BANK
Grade 10
Question:
Ritu can row downstream $20$ km in $2$ hours, and upstream $4$ km in $2$ hours. Find her speed of rowing in still water and the speed of the current.
Step-by-Step Solution
Key Concept: Compute the downstream and upstream speeds directly from distance/time, then use (speed in still water + current speed) for downstream and (speed in still water − current speed) for upstream.
Downstream speed $=\dfrac{20}{2}=10$ km/h; upstream speed $=\dfrac{4}{2}=2$ km/h. [1.0 Mark]
Let $x=$ speed in still water, $y=$ speed of current. Downstream: $x+y=10$ — (1). Upstream: $x-y=2$ — (2). [1.5 Marks]
Adding (1) and (2): $2x=12\Rightarrow x=6$. [1.5 Marks]
Substituting into (1): $6+y=10\Rightarrow y=4$. So Ritu's speed in still water is $6$ km/h and the speed of the current is $4$ km/h. [1.0 Mark]
Correct Answer:
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