CBSE Class 10 Mathematics Standard sample paper 2025-26: question 27

Hints

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Step-by-step solution

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1. For the fewest rooms, each room must hold the greatest possible number of teachers, so we need the HCF of 36, 60 and 84.
   $36=2^2\times 3^2$, $60=2^2\times 3\times 5$, $84=2^2\times 3\times 7$.
   HCF $=2^2\times 3=12$.

   1½ marks

2. Number of rooms $=\frac{36}{12}+\frac{60}{12}+\frac{84}{12}=3+5+7$

   1 mark

3. $=15$. So the minimum number of rooms required is 15.

   ½ mark

Answer: 15 rooms

Revise the chapter

• Chapter: Real Numbers (notes, formulas, where marks are lost and every past question)