MathsCBSE Class 10 · Basic · Board exam 2025, set 430/6/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Basic 2025: question 28

Set in the CBSE Class 10 board exam of 2025, paper 430/6/1, section C, question 28, for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q28 · 3 marks · Short answerCompetency-basedReal Numbers

Three measuring rods are of lengths 120 cm, 100 cm and 150 cm. Find the least length of a fence that can be measured an exact number of times, using any of the rods. How many times each rod will be used to measure the length of the fence?

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/6/1.

Hints

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

Hint 1

The fence length must be exactly divisible by each rod length — is that an HCF or LCM idea?

Hint 2

Find the LCM by prime factorisation, then divide it by each rod length.

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.

The required length must be a multiple of all three rod lengths, so we need their LCM.
$120 = 2^{3} \times 3 \times 5$ , $100 = 2^{2} \times 5^{2}$ , $150 = 2 \times 3 \times 5^{2}$
1½ marks
LCM $= 2^{3} \times 3 \times 5^{2} = 600$ . So the least length of the fence is 600 cm (= 6 m).
1 mark
Number of times each rod is used: $600 \div 120 = 5$ , $600 \div 100 = 6$ , $600 \div 150 = 4$ .
½ mark

Answer: 600 cm; the rods are used 5, 6 and 4 times respectively

Where the marks are

Correct prime factorisation of 120, 100, 150 (1½ marks)
LCM = 600 cm as least length (1 mark)
Rods used 5, 6 and 4 times (½ mark)

Revise the chapter

Chapter: Real Numbers (notes, formulas, where marks are lost and every past question)
Topic: HCF and LCM by Prime Factorisation

Practise this chapterBoard-style questions from Real Numbers, one at a time, marked against the answer key and marking points.Back to the full paper2025 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.

CBSE Class 10 Mathematics Basic 2025: question 28

Hints

Step-by-step solution

Revise the chapter

More questions from Real Numbers