P works 25% more efficiently than Q and Q works 50% more eff

P works 25% more efficiently than Q : Something that takes Q 5 days, takes P 4 days
Q works 50% more efficiently than R : Something that takes R 7.5 days, takes Q 5 days

P alone takes 50 days less than Q : For every 4 days P works, Q has to work an extra day. Hence P alone can do it in 200 days and Q alone in 250 days and hence R alone in 375 days

P works for 60 days --> 60/200 work done => 30%
Q works for 125 days --> 125/250 work done => 50%
20% work left ... R alone will take 20% * 375 = 75 days

Answer is (B)

I don't understand the explanation.
"P is 25% more efficient..hence he will take 100/125 * time taken by Q"
why is the rate 100/125?

Rate and time is inversely proportional.
Question says P is 25% more efficient than Q. This means P is 5/4 of Q's rate.
Work rate of P is 5/4 of Q.
Since time is inversely proportional to workrate,Time by P is 4/5 of time taken by Q=100/125 of Time taken by Q.

It's a question from a math book. I don't think you should worry too much about it.

True MariaBez, its a question from Indian Study material. But similar question that demands same approach can be seen in real GMAT.
Iits always better to know the approach. This can be solved easily in 1.25 mins if u are good in multiplication and division. wat takes u more time is the approach. do more practice questions and once u ace the approach and techniques, u are through.

Cleetus, good point! I decided to return to this question and try to solve it one more time. You're absolutely right. The more you practice, the quicker you will come up with solutions on real gmat.
Thank you!!

Good to know that.
Most of the questions posted in here are really worth solving and the solution explained here by GMAT Wizards here gives u different approach to a single question. Also do come up with as many good questions u can and see how those questions are dealt by many club members.

I have posted only selected questions which really need different approach that could help u in real GMAT.

Cleetus

Nice question. Yea the calculations take up a lot of time but the efficiency will increase with practice I guess. The concept of increased efficiency and the inverse relationship between time and work rate confused me.

Hi shrouded1

Please explain the following part of your explanation

P alone takes 50 days less than Q : For every 4 days P works, Q has to work an extra day. Hence P alone can do it in 200 days and Q alone in 250 days and hence R alone in 375 days

Rgds
Prasannajeet

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!!!

Don't bother buddy, This problem is perhaps from Indian CAT or XAT. I have never seen such problems in GMAT quant - There is lot of calculation involved.

However, for the curiosity, below is the solution.

Statement 1 :- P works 25% more efficiently than Q ---------> P takes 20 % less time than Q takes.
Statement 2 :- Q works 50% more efficiently than R ---------> Q takes 33.33% less time than R Takes.

Note 1 :- These are standard ratios and need to remember.
For Reference :-
If A is 10% greater than B, then B is 9.09% lesser than A
If A is 15% greater than B, then B is 13% lesser than A
If A is 20% greater than B, then B is 16.67% lesser than A
If A is 25% greater than B, then B is 20% lesser than A
If A is 30% greater than B, then B is 23% lesser than A
If A is 40% greater than B, then B is 28% lesser than A
If A is 50% greater than B, then B is 33.33% lesser than A
If A is 60% greater than B, then B is 37.50% lesser than A

Note 2 :- These are extremely useful in Time, Speed, and Distance. e.g. If you increase the speed by 10%, then time will be reduced by 9.09% (When the distance is constant)

Back to the Question........

let's Assume that R takes 100% time, So Q will take 66.67% time, and P will take 53.35% time.

Statement 3 :- P alone takes 50 days less than Q alone. ---------> We already know that Q's time is 66.67% and P's time is 53.35%, So P is taking (66.67 - 53.35) = 13.35 less time, which is equivalent to 50 days.

So if 13.35% time is equivalent to 50 days then 100% time (Which is R's) will be equivalent to 374 days -----------------------------{This can be derived using Unitary Method.

Remember this as if 13.35% belongs to 50 then 100% belongs to what? In equation it will be \(\frac{50}{13.35%} \frac{100}{?}\) -------- Direct multiplication will give the answer as 374 days.}

So We have the following
R takes 374 days to finish work alone.
Q takes 250 days to finish work alone.
P takes 200 days to finish work alone.

Now we can derive that
R finishes \(\frac{100}{374} = 0.26%\) work in a day working alone. ------[ We know, Total work always equals 100%]
Q finishes \(\frac{100}{250} = 0.40%\) work in a day working alone. ------[ We know, Total work always equals 100%]
P finishes \(\frac{100}{200} = 0.50%\) work in a day working alone. ------[ We know, Total work always equals 100%]

Statement 4 :- If, in this project P alone works for 60 days
P is completing 0.50% work in a day and he worked for 60 days, So he must have completed 30% of the work.

Statement 5 :- and then Q alone works for 125 days,
Q is completing 0.40% work in a day and he worked for 125 days, So he must have completed 50% of the work.

Now P and Q completed 50 + 30 = 80% work and we are left with only 20% work, which is to be completed by R

Question :- in how many days can R alone complete the remaining work? -------> \(\frac{20%}{0.26%} = 75 days\) approximately. Choice B

Hope That Helps.

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 = ½ part of work

So, P and Q did = 3/10 + ½ = 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)
…………….

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.

P = (15/8R)
Q= (3/2R)
R= 1/R ...............These are the rates of work given in the stimulus

let Q takes 't' days to complete a work
Hence, P takes 't-50'

(15/8R) * (t-50) = (3/2R) * t

=> t=250 days

Total work required is = (15/8R) * (250-50) = 375/R

P completes work = 375/2R in 60 days
Q completes work = 225/2R in 125 days

Hence R will complete

375/R - [275/2R + 375/2R]

Hence 75

TGC: IT seemed you swap the work for P and Q

Total work required is = (15/8R) * (250-50) = 375/R

P completes work = (15/8R)*60=225/2R in 60 days
Q completes work = (3/2R)*125=375/2R in 125 days

Hence R will complete

375/R - [275/2R + 375/2R]

Hence 75

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