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A lending library… (Class 10 Maths Basic SQP 2023-24, Q28b)

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MathsCBSE Class 10 · Basic · Sample paper, session 2023-24 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic sample paper 2023-24: question 28(b)

From the official CBSE sample question paper for 2023-24, section C, question 28(b), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q28(b) · 3 marks · Short answerCompetency-basedPair of Linear Equations in Two Variables

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs. 27 for a book kept for seven days, while Susy paid Rs. 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

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

Hint 1

The fixed charge covers 3 days. How many extra days did each person keep the book?

Hint 2

Saritha paid for 4 extra days and Susy for 2. Subtract the two equations to eliminate the fixed charge.

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.

  1. Let the fixed charge for the first 3 days be Rs and the charge for each extra day be Rs .

    ½ mark

  2. Saritha (7 days = 3 + 4 extra days): ...(1)
    Susy (5 days = 3 + 2 extra days): ...(2)

    ½ mark

  3. Subtracting (2) from (1):

    1 mark

  4. Substituting in (2):
    Fixed charge = Rs 15; charge for each extra day = Rs 3.

    1 mark

Answer: Fixed charge = Rs 15; extra charge = Rs 3 per day

Where the marks are

  • Defines the variables (1/2 mark)
  • Forms and (1/2 mark)
  • Finds (1 mark)
  • Finds and states the answer (1 mark)

Revise the chapter

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 paperSample paper 2023-24 (Basic): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.