Maths · Algebra · chapter 3 of 14
Class 10 Maths Chapter 3: Pair of Linear Equations in Two Variables case study question with answers
One case-based question of the kind the board asks in Section E: a passage and a figure, then 3 parts worth 4 marks in all, with the answer and the marking scheme for each. Written from the NCERT chapter.
Case study · 4 marks
Two courier services in Jaipur price parcels by weight. Service P charges ₹40 for booking plus ₹20 for each kilogram. Service Q charges ₹10 for booking plus ₹30 for each kilogram. A shopkeeper drew the graph of charge y (in ₹) against weight x (in kg) for both services, shown in the figure, to decide which to use.
Part 1 · 1 mark
The pair of equations for the two services is
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Answer: (a) y = 20x + 40 and y = 30x + 10
Charge = booking + rate × weight: P is y = 20x + 40, Q is y = 30x + 10.
Part 2 · 1 mark
From the graph, the weight for which both services charge the same is
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Answer: (a) 3 kg
The lines cross at (3, 100): at 3 kg both charge ₹100. 100 is the charge, not the weight.
Part 3 · 2 marks
Solve the pair algebraically and verify the crossing point read from the graph.
Answer and marking scheme
Substitute y = 20x + 40 into y = 30x + 10: 20x + 40 = 30x + 10, so x = 3 and y = 100. Check in the words: P charges 40 + 60 = ₹100 and Q charges 10 + 90 = ₹100 for 3 kg.
- substitutes and gets x = 3 (1)
- y = 100, checked against both services (1)
Or
Which service is cheaper for a 5 kg parcel, and by how much?
Answer and marking scheme
P: 40 + 20 × 5 = ₹140. Q: 10 + 30 × 5 = ₹160. P is cheaper by ₹20 (beyond 3 kg, P's line lies below Q's).
- both charges ₹140 and ₹160 (1)
- P cheaper by ₹20 (1)