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Q.

A school has 8 periods a day each of 35 minutes duration. How long would each period be, if the school has 7 periods a day, assuming the number of school hours to be the same?

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a

20 minutes

b

30 minutes

c

40 minutes

d

50 minutes

answer is C.

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Detailed Solution

Given that,
A school has 8 periods a day each of 35 minutes duration.
We have to find the duration of each period if the school has 7 periods a day.
We know that two variables are said to be inversely proportional if and only if they are directly proportional to one another's reciprocal. If

x and y

are two variables in inverse variations, then

x y = k,

where k is a proportionality constant.
Here, if the number of periods decreases, then class duration will increase, so it is in the inverse proportion.
Let us make a table as shown below:

Number of periods per day $(x)$	Duration of each period in minutes $(y)$
$x 1 = 8$	$y 1 = 35$
$x 2 = 7$	$y 2 =$ ?

Using the relation of inverse proportion

x 1 y 1 = x 2 y 2

, we get,

x 1 y 1 = x 2 y 2

⇒ y 2 = x 1 y 1 x 2 ⇒ y 2 = 8 × 35 7

∴ y 2 = 40

Thus, each period would be of 40 minutes.
Hence, option 3 is correct.

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