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Q.

A rectangular courtyard is $20 m 16 cm$ long and $15 m 60 cm$ broad. It is to be paved with square stones of the same size. What is the least possible number of such stones?

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a

5464

b

5400

c

5600

d

5460

answer is D.

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Detailed Solution

We have been given,
Breadth of the rectangular Courtyard = 15m 60 cm.
Converting meters into ‘cm’ using 1 m = 100 cm,
15m 60 cm = 1560 cm.
Calculating the prime factors of 2016 and 1560.

2016 = 2 \times 2 \times 2 \times 2 \times 2 \times 3 \times 3 \times 7

1560 = 2 \times 2 \times 2 \times 3 \times 5 \times 13

The common factors of 2016 and 1560,

\Rightarrow

2 × 2 × 2 × 3

\Rightarrow

24
Therefore, the H.C.F is 24.
We have,
Least possible number of stones to be paved = Area of a rectangular courtyard ÷ Area of a square stone
Substituting the values,

\Rightarrow (2016 \times 1560) \div {(24)}^{2}

\Rightarrow 5460

Therefore, the least possible number of such stones to be paved is 5460.
Hence, option 4 is correct.

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