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The number of planks of dimensions $\left ( 4\; m\times 50\; cm \times 20\; cm \right )$ that can be stored in a pit which is $16\; m$ long, $12\; m$ wide and $4\; m$ deep is

(A) $1900$

(B) $1920$

(C) $1800$

(D) $1840$

Answers (1)

Answer (B)

We can see that both the plank and pit will be in the form of a cuboid.

Volume of a cuboid $=l \times b \times h$

Where l is its length, b is breadth and h is height.

Given dimensions of plank $=\left ( 4\; m\times 50\; cm \times 20\; cm \right )$

We know that, $1m=100 cm$

So, Dimension of plank $=\left ( 4\; m\times 0.5\; m \times 0.2\; m \right )$

Volume of plank $=4\; m\times 0.5\; m \times 0.2\; m=4\; m^{3}$

Now, Dimensions of pit $=\left ( 16\; m\times 12\; m \times 40\; m \right )$

Volume of pit $=16\; m\times 12\; m \times 40\; m =7680\; m^{3}$

Thus number of planks that can be fitted into the pit $=\frac{\text {Volume of Pit}}{\text {Volume of plank}}$

$=\frac{7680}{4}$

$=1920$

This is option (B) is the correct.

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infoexpert23

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