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A gardener is digging a plot of land. As he gets tired, he works more slowly. After 't' minutes he is digging at a rate of ( 2 t ) square metres per minute. How long will it take him to dig an area of ( 40 ) square metres?

Options

  1. A( 10 ) minutes
  2. B( 40 ) minutes
  3. C( 100 ) minutes
  4. D( 30 ) minutes

Correct answer

C. ( 100 ) minutes

Step-by-step solution

Given that, d A d t = 2 t d A= 2 t d t Integrating both the sides, we have d A= 2 d t t A=2 2 t +C When t=0 we have C=0 So, 4 t =40 t=10²=100 ~min

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