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A field is $150 m$ long and $100 m$ wide. A plot (outside the field) 50 m long and $30 m$ wide is dug to a depth of $8 m$ and the earth taken out from the plot is spread evenly in the field. By how much is the level of field raised?

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0.8 m

7.2 m

0.5 m

2.4 m

answer is A.

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Detailed Solution

It is given a field of 150 m length and 100 m width and a plot of 50 m length and 30 m width is dug to a depth of 8 m.
Consider the level of field raised be h.
Calculate the volume of the earth dug out,

V = 50 × 30 × 8 ⇒ V = 12000 m 3 ......... 1

Calculate the volume of the earth raised in the field,

V = 150 × 100 × h ⇒ V = 15000 h ......... 2

Comparing equation

1

and

2

15000 h = 12000

Divide both sides by 15000,

h = 1200015000

⇒

h = 0.8

m

So the level of the field raised is 0.8

m

.
Hence option (1) is correct.

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