Working alone, three persons, P, Q and R can do a certain job

Question

Working alone, three persons P, Q, and R can do a certain job in 10, 12, and 15 hours respectively. What is the ratio of the maximum and minimum time taken to complete the job, if at every hour, at least 1 person must work?

A.

B.

C.

D.

E.

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A.  1:3
 B.  1:2
 C.  1:1
 D.  3:1
 E.  15:4

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MayankSingh · Answer

Let total Work unit be 60
So, P will do 6 unit/Hr (As total time taken to complete work is 10 Hrs: 10*6 unit=60)
Similarly, Q = 5 Units/Hr & R = 4 Units/Hr
For Min Time all three should work Together
Together P,Q & R will do =6+5+4 Unit=15 units/Hr
Therefore Min. Time taken= 60/15= 4 Hrs

Similarly for max time only one of them work (the slowest one) i.e R
Therefore, Max time taken=60/4=15 Hrs.

Req. Ratio=15:4 (Ans E)

praveenkuragodi · Answer

Three people are working to complete a job, then the shortest time taken to complete if at least 1 person is working then the shortest time is when all the 3 are working together which gives us 4 hours. Now the longest time would be when the person with the longest time is working alone ie 15 hours. Therefore the ratio is 15:4.

sumit411 · Answer

Max time to minimum time means numerator is bigger than denominator.

Eliminate A, B, C

Together they can finish the work in 4 hours ( add to their rates). This is minimum time.

Maximum time taken is - - > when the guy with least efficiency works =15 hours
Answer is E

Thank you = Kudos

Abhinav kumar · Answer

if all of them work together they will take 4 hrs that is the minimum time taken.
and if the guy who take maximum time work alone that is maximum time taken that is 15
max:min is 15:4 ans E

CounterSniper · Answer

time taken will be minimum when all three will work simultaneously = 1/10 + 1/15 + 1/12 = (6+4+5)/60 = 15/60 = 4 hours
time taken will be maximum when R will work alone = 15 hours 
max / min = 15/4

sushforgmat · Answer

This is a simple but good question. 
Thanks  EgmatQuantExpert

ScottTargetTestPrep · Answer

The maximum amount of time to complete the job is if R , the slowest worker, works alone, and it will take him 15 hours to complete it.

The minimum amount of time to complete the job is if all three people work together, and it will take them 1/(1/10 + 1/12 + 1/15) = 1/(6/60 + 5/60 + 4/60) = 1/(15/60) = 60/15 = 4 hours to complete it.

Therefore, the ratio is 15:4.

Answer: E

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Working alone, three persons, P, Q and R can do a certain job

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