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Q.

The area of the rectangle field is 3584 $m^{2}$ and its length is 64 $m .$ A boy runs around the field at a rate of 6 $km h r^{- 1}$ . How long will it take to go 5 rounds around it?

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a

720 minutes

b

33 minutes

c

12 minutes

d

None of these

answer is C.

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Detailed Solution

Concept- Using the given area and length of the rectangular field we will get the breadth of the rectangular field and then we will find the perimeter of round, then applying unitary method we will get the perimeter of 5 rounds, and this will be the distance, and as the speed is already given in the question, we will convert speed in meter per second as our distance is in meters ,and then apply time formula to find the required answer.
Area A of the rectangular field

= 3584 m^{2}

Length of the rectangular field

= 64 m

We know,

area = length \times breadth

\Rightarrow 3584 = 64 \times breadth

\Rightarrow breadth = 56 m

We know,
perimeter P of the rectangular field

=

2 (length + breadth)

\Rightarrow P = 2 (64 + 56)

\Rightarrow P = 240 m

Perimeter of 1 round is 240

m

Therefore, for 5 rounds

240 \times 5 = 1200 m

Speed is given 6

km h r^{- 1}

,
Speed in

m s^{- 1} = 6 \times \frac{5}{18} = \frac{5}{3} {m s^{- 1}}^{}

Time = \frac{Distance}{Speed}

, we get

\Rightarrow Time = \frac{1200}{\frac{5}{3}}

\Rightarrow Time = \frac{1200 \times 3}{5}

\Rightarrow Time = 240 \times 3

\Rightarrow Time = 720 seconds

720 seconds in minutes

= \frac{720}{60} = 12 minutes

Therefore, the boy will take 12 minutes to complete 5 rounds.
Hence, the correct answer is option 3.

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