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Two people are 16 km apart on a… (Class 10 Maths 2023, Q29)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/5/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2023: question 29

Set in the CBSE Class 10 board exam of 2023, paper 30/5/1, section C, question 29, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q29 · 3 marks · Short answerCompetency-basedPair of Linear Equations in Two Variables

Two people are 16 km apart on a straight road. They start walking at the same time. If they walk towards each other with different speeds, they will meet in 2 hours. Had they walked in the same direction with same speeds as before, they would have met in 8 hours. Find their walking speeds.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/5/1.

Hints

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

Hint 1

When they walk towards each other, the distances they cover add up to 16 km.

Hint 2

When they walk in the same direction, the faster one must cover 16 km more than the slower one before they meet.

Hint 3

You will get two linear equations; add them to find x.

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 speeds be km/h and km/h with . Walking towards each other, together they cover 16 km in 2 h:
    ……(i)

    1 mark

  2. Walking in the same direction, the faster one gains 16 km in 8 h:
    ……(ii)

    1 mark

  3. Adding (i) and (ii): ; then from (i), .
    Their walking speeds are 5 km/h and 3 km/h.

    1 mark

Answer: 5 km/h and 3 km/h

Where the marks are

  • Forms 2x + 2y = 16 for the case of walking towards each other (1 mark)
  • Forms 8x − 8y = 16 for the case of walking in the same direction (1 mark)
  • Solves to get x = 5 km/h (½ mark) and y = 3 km/h (½ 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 30/5/1 (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.