Skip to content

Lokesh, a production… (Class 10 Maths Basic 2023, Q37)

questionbuddy.in/q/cbse-10-maths-2023-430-6-1-q37-lokesh-production-manager-mumbai-hires

MathsCBSE Class 10 · Basic · Board exam 2023, set 430/6/1 · 4 marks · Case-based

CBSE Class 10 Mathematics Basic 2023: question 37

Set in the CBSE Class 10 board exam of 2023, paper 430/6/1, section E, question 37, for 4 marks. Try it first; the hints and our step-by-step solution are below.

Q37 · 4 marks · Case-basedCompetency-basedPair of Linear Equations in Two Variables

Lokesh, a production manager in Mumbai, hires a taxi everyday to go to his office. The taxi charges in Mumbai consists of a fixed charges together with the charges for the distance covered. His office is at a distance of 10 km from his home. For a distance of 10 km to his office, Lokesh paid ₹ 105. While coming back home, he took another route. He covered a distance of 15 km and the charges paid by him were ₹ 155.

Based on the above information, answer the following questions:

  1. (i)

    What are the fixed charges?

    1 mark
  2. (ii)

    What are the charges per km?

    1 mark
  3. (iii)

    If fixed charges are ₹ 20 and charges per km are ₹ 10, then how much Lokesh have to pay for travelling a distance of 10 km?

    2 marks

  4. OR

    (iii)

    Find the total amount paid by Lokesh for travelling 10 km from home to office and 25 km from office to home. [Fixed charges and charges per km are as in (i) & (ii).]

    2 marks

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/6/1.

Hints

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

Hint 1

Use one variable for the fixed charge and another for the charge per km.

Hint 2

Write one equation for each trip, then subtract them to remove the fixed charge.

Hint 3

For the two-way trip, the fixed charge is paid twice.

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. (i) Let the fixed charge be ₹ x and the charge per km be ₹ y.
    Then ...(1) and ...(2)

    ½ mark

  2. Subtract (1) from (2): , so .
    Put this in (1): .
    Fixed charge = ₹ 5

    ½ mark

  3. (ii) From the working above, . Charge per km = ₹ 10

    1 mark

  4. (iii)(a) Amount = fixed charge + 10 × charge per km

    1 mark

  5. 1 mark

  6. (iii)(b) Total amount

    1 mark

  7. 1 mark

Answer: (i) ₹ 5; (ii) ₹ 10 per km; (iii)(a) ₹ 120; (iii)(b) ₹ 360

Where the marks are

  • Forms the equations and (½ mark)
  • Fixed charge = ₹ 5 (½ mark)
  • Charge per km = ₹ 10 (1 mark)
  • (iii)(a) Writes (1 mark); gets ₹ 120 (1 mark)
  • (iii)(b) Total = (1 mark); gets ₹ 360 (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 paper2023 board paper, set 430/6/1 (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.