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Question 16.

Teams A, B, and C consist of five, eight, and ten members, respectively, such that every member within a team is equally productive. Working separately, teams A, B, and C can complete a certain job in 40 hours, 50 hours, and 4 hours, respectively. Two members from team A, three members from team B, and one member from team C together start the job, and the member from team C leaves after 23 hours. The number of additional member(s) from team B, that would be required to replace the member from team C, to finish the job in the next one hour, is

A
B
C
D
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Text Explanation

Let the per hour productivity of each member from teams A, B, and C, be $a$, $b$, and $c$ units respectively.

Let $W$ be the total units of work that each of the teams does. We have:

$W = 40*5*a = 50*8*b = 4*10*c$

This gives, $a= \dfrac{W}{200}$, $b= \dfrac{W}{400}$, and $c = \dfrac{W}{40}$

When two members from team A, three members from team B, and one member from team C together start the job, the total per hour productivity for the first 23 hours will be;

$\dfrac{2W}{200} + \dfrac{3W}{400} + \dfrac{W}{40} = \dfrac{17W}{400}$

In 23 hours, the work done will be $\dfrac{23*17W}{400} = \dfrac{391W}{400}$

The remaining work, after 23 hours, is $W - \dfrac{391W}{400} = \dfrac{9}{400}$

The current per hour efficiency of the group that comprises members from only teams A and B, is $\dfrac{2W}{200} + \dfrac{3W}{400} = \dfrac{7W}{400}$

In the next hour, the members from A and B will finish $\dfrac{7W}{400}$ units of work and $\dfrac{9W}{400}-\dfrac{7W}{400} = \dfrac{2W}{400}$ units of work would remain.

This work has to be finished by newly added members from team B in one hour, therefore, the number of new members required from team B would be $\dfrac{2W}{400} \div \dfrac{W}{400} = 2$

Option B is the correct answer.

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