Skip to content

Places A and B are 180… (Class 10 Maths SQP 2024-25, Q32B)

questionbuddy.in/q/cbse-10-maths-2024-25-sqp-standard-q32b-places-apart-highway-car-starts

MathsCBSE Class 10 · Standard · Sample paper, session 2024-25 · 5 marks · Long answer

CBSE Class 10 Mathematics Standard sample paper 2024-25: question 32(B)

From the official CBSE sample question paper for 2024-25, section D, question 32(B), for 5 marks. Try it first; the hints and our step-by-step solution are below.

Q32(B) · 5 marks · Long answerCompetency-basedPair of Linear Equations in Two Variables

Places A and B are km apart on a highway. One car starts from A and another from B at the same time. If the car travels in the same direction at different speeds, they meet in hours. If they travel towards each other with the same speeds as before, they meet in an hour. What are the speeds of the two cars?

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

Hints

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

Hint 1

Let the two speeds be and . When moving in the same direction, the faster car gains on the slower one; when moving towards each other, the distances add.

Hint 2

Form and , then solve the pair.

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 speed of the car from A be km/h and the speed of the car from B be km/h, with .

  2. Same direction: the car from A catches up with the car from B in 9 hours, so the difference in the distances covered equals AB:
    …(i)

    2 marks

  3. Towards each other: they meet in 1 hour, so the sum of the distances covered equals AB:
    …(ii)

    2 marks

  4. Adding (i) and (ii): . Then .
    The speeds of the cars are 100 km/h (from A) and 80 km/h (from B).

    1 mark

Answer: 100 km/h and 80 km/h

Where the marks are

  • Forms the equation for the same-direction case (2 marks)
  • Forms the equation for the opposite-direction case (2 marks)
  • Solves to get the speeds 100 km/h and 80 km/h (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 2024-25 (Standard): 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.