How many planks of dimensions $5 m \times 25 c m \times 10 c m$ can be stored in a pit which is $20 m$ long, $6 m$ wide and $80 c m$ deep?

728

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748

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768

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788

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Solution

The correct option is C 768
The dimensions of a plank are
Length, $l = 5 m = 500 c m$ ,
Breadth, $b = 25 c m$ ,
Height, $h = 10 c m$ ,
We know that,
Volume of the plank = $l \times b \times h$
= $500 \times 25 \times 10$ = $125000 c c$

The dimensions of the pit are
Length, $l = 20 m = 2000 c m$ ,
Breadth, $b = 6 m = 600 c m$ ,
Height, $h = 80 c m$ ,
We know that,
Volume of the pit = $l \times b \times h$
= $2000 \times 600 \times 80$ = $96000000 c c$

Also, note that the length of the pit is a multiple of the length of a plank. The same holds true for other two dimensions. In such a case:

The number of planks that can be stored = Volume of the pit/Volume of a plank = $96000000 / 125000$ = $768$

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