MathsCBSE Class 10 · Basic · Board exam 2025, set 430/4/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Basic 2025: question 36

Set in the CBSE Class 10 board exam of 2025, paper 430/4/1, section E, question 36, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q36 · 4 marks · Case-basedCompetency-basedPair of Linear Equations in Two Variables

A telecommunication company came up with two plans– plan A and plan B for its customers. The plans are represented by linear equations where ' $t$ ' represents the time (in minutes) bought and ' $C$ ' represents the cost. The equations are: Plan A: $3 C = 20 t$ ; Plan B: $3 C = 10 t + 300$ . Based on above information, answer the following questions. (Image: a calculator and a mobile tower.)

(i)
If you purchase plan B, how much initial amount you have to pay?
1 mark
(ii)
Charu purchased plan A. How many minutes she bought for ₹ 250?
1 mark
(iii)(a)
At how many minutes, do both the plans charge the same amount? What is that amount?
2 marks
OR
(iii)(b)
Which plan is better if you want to buy 60 minutes? Give reason for your answer.
2 marks

Figure in the paper: Decorative picture of a calculator in front of a mobile phone tower with antennas and dishes. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/4/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

The initial amount is what you pay before using any minutes. Which value of $t$ is that?

Hint 2

For (ii) and (iii), substitute the known value into the right equation. When the plans cost the same, their $C$ values are equal.

Hint 3

For (iii)(b), find $C$ for both plans at $t = 60$ and compare the two costs.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

(i) The initial amount is the cost when no minutes are used. Put $t = 0$ in Plan B: $3 C = 10 (0) + 300 = 300 \Rightarrow C = 100$ . So ₹100 must be paid initially.
1 mark
(ii) For Plan A put $C = 250$ : $3 \times 250 = 20 t \Rightarrow 750 = 20 t \Rightarrow t = 37.5$ . Charu bought 37.5 minutes.
1 mark
(iii)(a) Both plans cost the same when their values of $3 C$ are equal: $20 t = 10 t + 300 \Rightarrow 10 t = 300 \Rightarrow t = 30$ minutes.
1 mark
(iii)(a) Amount: $C = \frac{20 \times 30}{3} = ₹200$ . Both plans charge ₹200 for 30 minutes.
1 mark
(iii)(b) Plan A at $t = 60$ : $3 C = 20 \times 60 = 1200 \Rightarrow C = ₹400$ .
½ mark
(iii)(b) Plan B at $t = 60$ : $3 C = 10 \times 60 + 300 = 900 \Rightarrow C = ₹300$ .
½ mark
(iii)(b) Plan B is better for 60 minutes, because it costs ₹100 less than Plan A.
1 mark

Answer: (i) ₹100; (ii) 37.5 minutes; (iii)(a) 30 minutes, ₹200; (iii)(b) Plan B (₹300 against ₹400, saves ₹100)

Where the marks are

Puts $t = 0$ in Plan B and gets ₹100 (1 mark)
Solves $750 = 20 t$ to get $t = 37.5$ minutes (1 mark)
Equates the plans to get $t = 30$ minutes (1 mark)
Finds the common amount ₹200 (1 mark)
Cost under Plan A for 60 minutes is ₹400 (½ mark)
Cost under Plan B for 60 minutes is ₹300 (½ mark)
Concludes Plan B is better, with the ₹100 saving as the reason (1 mark)

Revise the chapter

Chapter: Pair of Linear Equations in Two Variables (notes, formulas, where marks are lost and every past question)
Topic: Graphical Method of Solving Linear Equations

Practise this chapterBoard-style questions from Pair of Linear Equations in Two Variables, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 430/4/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2025: question 36

Hints

Step-by-step solution

Revise the chapter

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