Maths · Number systems · chapter 1 of 14
Class 10 Maths Chapter 1: Real Numbers case study question with answers
One case-based question of the kind the board asks in Section E: a passage, then 3 parts worth 4 marks in all, with the answer and the marking scheme for each. Written from the NCERT chapter.
Case study · 4 marks
The courtyard of an old haveli in Jaipur is being re-laid. It is a rectangle 1080 cm long and 756 cm wide. The contractor, Harish, wants to use square marble tiles, all of the same size, with no tile cut. To keep the joints few, he wants the tiles as large as possible. Before ordering, he writes both measurements as products of primes, as his daughter showed him: 1080 = 23 × 33 × 5.
Part 1 · 1 mark
The prime factorisation of 756 is
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Answer: (a) 22 × 33 × 7
756 = 2 × 378 = 22 × 189 = 22 × 33 × 7. 23 × 32 × 7 is 504; the other two contain 21 and 14, which are not prime.
Part 2 · 1 mark
The side of the largest square tile Harish can use is
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Answer: (a) 108 cm
HCF = smallest powers of the common primes 2 and 3: 22 × 33 = 108 cm. 54 and 36 are common factors but not the greatest; 7560 is the LCM.
Part 3 · 2 marks
How many tiles does he need?
Answer and marking scheme
Along the length 1080 ÷ 108 = 10 tiles; along the width 756 ÷ 108 = 7 tiles. Number of tiles = 10 × 7 = 70.
- 10 tiles along the length and 7 along the width (1)
- 70 tiles (1)
Or
Using the HCF, find the LCM of 1080 and 756 without listing prime powers again.
Answer and marking scheme
HCF × LCM = 1080 × 756, so LCM = (1080 × 756) ÷ 108 = 816480 ÷ 108 = 7560.
- uses LCM = (1080 × 756) ÷ HCF (1)
- LCM 7560 (1)