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Q.

A contractor estimates that 4 persons could rewire a house in 5 days. If he uses 5 persons instead of 4, how long should they take to complete the job?
 


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a

7 days

b

6 days

c

5 days

d

4 days 

answer is D.

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Detailed Solution

Given that,
4 persons rewire a house in 5 days.
We have to find the number of days such that 5 persons rewire the same house.
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
xy=k,   where k is a proportionality constant.
Here, if the number of people increases, then the number of days they require to complete the house decreases, 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 =4  

y 1 =5  

x 2 =5  

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 = 4×5 5  
  ∴ y 2 =4  
Therefore, it will take 4 days to complete the same job.
Hence, option 4 is correct.
 
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