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Q.

The area of a square field is How long will a lady take to cross the field diagonally at the rate of

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a

1 hour 25 minutes

b

1 hour 15 minutes

c

1 hour 35 minutes

d

1 hour 45 minutes

answer is D.

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Detailed Solution

Concept: The area of the square is given by

a^{2}

, so we first consider the given data
By finding the value of

d^{2}

we can find the length of the diagonal of the square. This is twice the area of a square. You can simplify the formula to find the diagonal value. We found distance and velocity that allows us to find time using the relationship between distance and time.
First, consider the given data. That is, the area of the square is given by

.
You need to find the time it takes for the Queen to cross the field diagonally at the specified speed. Now, the diagonal length d of the square can be found by setting it equal to twice the area of the square. Consider the figure
Question Image

Question Image

So we get

Therefore, the diagonal length is 80m.
You need to find the time it takes to cross a length of 80 meters at a speed of

, so you can use the distance-time relationship.
This is

.
You also need to convert the units of velocity in the same way that you convert the units of diagonal length
Multiply the formula by

to convert km / h to m / min.
Therefore,

So get the time a woman needs for 1 hour and 45 minutes
Hence, the correct answer is 4) 1 hour 45 minutes

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