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Q.

Two persons could fit a new window in a house in 5 days. One of the persons fell ill before the work started. The time taken to complete the job is

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a

10 days

b

12 days

c

8 days

d

6 days

answer is A.

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Detailed Solution

Given that,
Two persons required 5 days to fit a window.
We have to find the time taken to complete the job by only one person.
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 people decreases, then the number of days they are required to complete the work increases, so it is in the inverse proportion.
Let us make table as shown below:

Number of people $(x)$	Number of days they required $(y)$
$x 1 = 2$	$y 1 = 5$
$x 2 = 1$	$y 2 =$ ?

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 = 2 × 5 1

∴ y 2 = 10

Therefore, 10 days would be needed to fit the windows by one person.
Hence, option 1 is correct.

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