MathsCBSE Class 10 · Standard · Board exam 2023, set 30/4/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2023: question 21

Set in the CBSE Class 10 board exam of 2023, paper 30/4/1, section B, question 21, for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21 · 2 marks · Very short answerReal Numbers

Two numbers are in the ratio 2 : 3 and their LCM is 180. What is the HCF of these numbers?

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 30/4/1.

Hints

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

Hint 1

Write the two numbers as $2 x$ and $3 x$ .

Hint 2

Their LCM is $6 x$ . Set it equal to 180 and solve for $x$ .

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.

Let the numbers be $2 x$ and $3 x$ . Since 2 and 3 are co-prime, $LCM = 6 x$ .
$6 x = 180 \Rightarrow x = 30$ .
1 mark
The numbers are $60$ and $90$ , so $HCF (60, 90) = 30$ .
1 mark
Therefore the HCF of the numbers is $30$ .

Answer: HCF = 30 (numbers 60 and 90)

Where the marks are

Takes the numbers as $2 x, 3 x$ , uses LCM $= 6 x = 180$ and gets $x = 30$ (1 mark)
Finds the numbers 60, 90 and their HCF $= 30$ (1 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 paper2023 board paper, set 30/4/1 (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.

CBSE Class 10 Mathematics Standard 2023: question 21

Hints

Step-by-step solution

Revise the chapter

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