Question : A room 16 m 5 cm long and 15 m broad is to be fitted with equal square tiles. How many numbers of the largest possible tiles are required so that they exactly fit?
Option 1: 10400
Option 2: 10700
Option 3: 10800
Option 4: 9800
Correct Answer: 10700
Solution : Length of room = 16m 5 cm = 1605 cm Width = 1500 cm 1605 = 3 × 5 × 107 1500 = 2 × 2 × 3 × 5 × 5 × 5 The largest side of the square tile = HCF of (1605,1500) = 15 cm Number of tiles = $\frac{1605×1500}{15×15}$ = 10700 Hence the correct answer is 10700.
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Question : The greatest possible length that can be used to measure exactly the lengths of 3 m 15 cm, 5 m, and 6 m 85 cm is:
Option 1: 9 cm
Option 2: 11 cm
Option 3: 7 cm
Option 4: 5 cm
Question : The radii of two circles are 5 cm and 3 cm. The distance between their centre is 24 cm. Then the length of the transverse common tangent is:
Option 1: $16$ cm
Option 2: $15\sqrt{2}$ cm
Option 3: $16\sqrt{2}$ cm
Option 4: $15$ cm
Question : The least number of five digits which is exactly divisible by 9, 12, 15, 25 and 27 is:
Option 1: 10800
Option 2: 10250
Option 3: 10700
Option 4: 10600
Question : Find the greatest possible length (in metres) that can be used to exactly measure the lengths 6 m, 5 m 25 cm and 12 m 50 cm.
Option 1: 0.25 m
Option 2: 0.75 m
Option 3: 0.90 m
Option 4: 0.35 m
Question : The longest rod that can be placed in a room is 12 metres long, 9 metres broad, and 8 metres high is:
Option 1: 27 m
Option 2: 19 m
Option 3: 17 m
Option 4: 13 m
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