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Pair of Linear Equations in Two Variables
RD Sharma
CBSE
Grade 10
Question:
The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of $10\text{ km}$, the charge paid is $₹105$ and for a journey of $15\text{ km}$, the charge paid is $₹155$. (i) What are the fixed charges and the charge per km? (ii) How much does a person have to pay for travelling a distance of $25\text{ km}$?
Step-by-Step Solution
Key Concept: Fixed charge $= x$, per km charge $= y$. (1) $x + 10y = 105$, (2) $x + 15y = 155$. Subtract: $5y = 50 \Rightarrow y = ₹10$ per km, $x = 105 - 100 = ₹5$ fixed charge. For $25\text{ km}$: $5 + 25(10) = 5 + 250 = ₹255$.
Equations: (1) $x + 10y = 105$, (2) $x + 15y = 155$. [1.0 Mark] Subtract (1) from (2): $5y = 50 \Rightarrow y = ₹10$ per km. [1.5 Marks] $x + 10(10) = 105 \Rightarrow x = ₹5$ fixed charge. [1.5 Marks] For $25\text{ km}$: Charge $= x + 25y = 5 + 25(10) = 5 + 250 = ₹255$. [1.0 Mark]
--- 🎯 Official CBSE Marking Scheme: Forming linear equations: 1.0 Mark Solving per km charge $y = ₹10$: 1.5 Marks Solving fixed charge $x = ₹5$: 1.5 Marks Calculating $25\text{ km}$ charge $= ₹255$: 1.0 Mark
Correct Answer:
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