WholeLottaLove wrote:
P works 25% more efficiently than Q and Q works 50% more efficiently than R. To complete a certain project, P alone takes 50 days less than Q alone. If, in this project P alone works for 60 days and then Q alone works for 125 days, in how many days can R alone complete the remaining work?
I am lost...start to finish I am totally lost. Could someone help me out on this? I have been staring at it for 30 minutes to no avail!!!
I am lost...start to finish I am totally lost. Could someone help me out on this? I have been staring at it for 30 minutes to no avail!!!
solution:
Ratio of efficiency, P:Q:R = (125/100) 150 : 150 : 100
Or, P:Q:R = 15:12:8
The more you effective the less time you need to work.
So working days is just reverse of the efficiency.
Here, For number of days, P:Q = 12:15 = 4:5 =8:10
And, Q:R= 8:12 = 2:3 = 10:15
So the ratio of working days for P:Q:R = 8:10:15
We can imagine now that to do 1 work P and Q need respectively 8x and 10x days.
According to the question, 10x 8x = 50
Or, x = 25 days
Finally, the ratio of working days for 1 full work , P:Q:R = 8x:10x:15x
Or, 8 25 : 10 25 : 15 25
Or, 200 : 250 : 375
P can do in 60days = 60/200 = 3/10 part of work
Q can do in 125days = 125/250 = part of work
So, P and Q did = 3/10 + = 4/5 parts of work
Remaining = 1 4/5 = 1/5 part of works have to be done by R .
R can do 1 work in 375 days
So R can do 1/5 part of work = 1/5 375 = 75 days (Answer)
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I elaborate all the things I did just to make it clear, but the problem is not so huge.
Just do these parts:
1.Evaluate efficiency ratio
2.Convert it by reversing into time ratio
3.Use the 50days information with the ratio
4.Then you can use normal work and rate formulas ,which I elaborately did here.