(Rates) Time and Work

Question

6 men can finish a piece of work in 2 hours. How long will 9 men take to finish the work if they can work only at 4/5th the capacity of the initial workers?

A. 5/2
B. 16/5
C. 3/2
D. 5/3
E. 2

Leadership · Answer

Hi,
Total man hours = 6*2= 12 Manhours
Now, the above 6 men are replaced by 9 men which are 4/5 or 0.8 capacity. New men will be- 9*0.8 - 7.2
New hours required - 12/7.2 = 1.67 or (5/3).  D  is correct choice

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sirihbs · Answer

If 6 people take 2 hours, then 9 people----(6*2)/9=4/3
If x takes 4/3 then 4/5th of X i.e. 0.8X takes-----(X*4/3)/(0.8X)=5/3

Raxit85 · Answer

Hi, Sjas31,

Can you please elaborate the last step.

New hours required - 12/7.2 = 1.67 or (5/3).

Regards,
Raxit T.

Leadership · Answer

This is the way I approach. 
12 is the total manhours required to finish a job. Hence, the new 7.2 Men will take - 12/7.2 hours to finish the same job.

CrackverbalGMAT · Answer

Hello Akrati,

The Unitary method is probably the best method to solve this question on Rates.

Let the total work done be 1 unit. Since 6 men can do 1 unit in 2 hours, it means that they work at the rate of ½ units per hour. This means that every man can work at the rate of  \frac{1}{12}  units per hour.

Working at this rate, 9 men can do ¾ units per hour. But, the question mentions that the group of 9 men work at  \frac{4}{5} th of the capacity (rate) of the 6-member group. This means that 9 men can do  \frac{4}{5} * \frac{(3}{4)}  = \frac{3}{5} units per hour.

When work is constant, time and rate are reciprocal of each other .

In this question, we have taken the work as 1 unit, which means we have kept it constant. For this work, the rate of 9 men is  \frac{3}{5}  units per hour. Therefore, the time taken to complete the entire work will be the reciprocal of  \frac{3}{5}  i.e.  \frac{5}{3}  hours.

The correct answer option is D.

Hope that helps!

(Rates) Time and Work

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