Q77 / 180 · KCET 2014 · Mathematics

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 \( \frac{2}{\sqrt{t}} \) square metres per minute. How long will it take him to dig an area of
\( 40 \) square metres?

  • A
    \( 10 \) minutes
  • B
    \( 40 \) minutes
  • Correct answer
    C
    \( 100 \) minutes
  • D
    \( 30 \) minutes

Solution

Given that, $\frac{d A}{d t}=\frac{2}{\sqrt{t}}$ $\Rightarrow d A=\frac{2}{\sqrt{t}} d t$ Integrating both the sides, we have $\int d A=\int \frac{2 d t}{\sqrt{t}}$ $\Rightarrow A=2 \cdot 2 \sqrt{t}+C$ When $t=0$ we have $C=0$ So, $4 \sqrt{t}=40$ $\Rightarrow t=10^{2}=100 \mathrm{~min}$

Hence, the correct answer is option: 'C'.

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