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Pair of Linear Equations in Two Variables
CH03 Question Bank
CBSE_CH03_QUESTION_BANK
Grade 10
Question:
Points $A$ and $B$ are $100$ km apart. Two cars start simultaneously from $A$ and $B$, travelling towards each other, and meet after $5$ hours. If instead they travel in the same direction (starting from the same points), the faster car catches up to the slower one after $25$ hours. Find the speed of each car.
Step-by-Step Solution
Key Concept: Form equations from 'towards each other' (relative speed = sum) and 'same direction' (relative speed = difference) scenarios.
Let the speeds be $x$ km/h and $y$ km/h ($x>y$). Moving towards each other: $5(x+y)=100\Rightarrow x+y=20$. [1.0 Mark]
Moving in the same direction, the gap closes at rate $(x-y)$: $25(x-y)=100\Rightarrow x-y=4$. [1.0 Mark]
Adding the two equations: $2x=24\Rightarrow x=12$; then $y=20-12=8$. So the speeds are $12$ km/h and $8$ km/h. [1.0 Mark]
Correct Answer:
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