Re: Time and Work #1

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.