Anurag@Gurome wrote:goyalsau wrote:The time taken by P to complete a piece of work is four times the time taken by Q. Q takes four times the time taken by R and R takes four times the time taken by S. When these four persons are divided into 2 pairs, the ratio of the times taken by the two pairs is 13 : 4. Find the pair, which takes less time to complete the work.
P, S
P, R
Q, R
Q, S
P, Q
I guess previous posters have identified their mistakes.
I'm providing only the solution here.
Say S takes 1 hour to complete the task
=> R takes 4 hrs
=> Q takes 16 hrs
=> P takes 64 hrs
In 1 hour,
- P does 1/64 of the total work
Q does 1/16 of the total work
R does 1/4 of the total work
S does whole of the total work
For option A, the 2 pairs are (P, S) and (Q, R)
- (P, S) does (1 + 1/64) = 65/64 of the total work in 1 hour
=> (P, S) takes 64/64 hrs to complete the work
(Q, R) does (1/4 + 1/16) = 5/16 of the total work in 1 hour
=> (Q, R) takes 16/5 hrs to complete the work
Ratio of times taken by the two pairs = (16/5)/(65/64) = 13/4
Thus our pair selection is correct and pair (P, S) takes the less time to complete the work.
The correct answer is A.
Note: In this case we didn't check the other options because while analyzing option A we got the correct answer. Otherwise we have to check till we get the correct one.
Nicely Explained Anurag !
I would just like to add few observation(s) here (which can potentially help to minimize the choices, in similar problems) :
S is the fastest member. I am listing the rates :
S-> 1
R -> 1/4
Q -> 1/4^2
S -> 1/4^3
Now, even if S does the work alone, and all the rest do it combined, S will be more than 3 times faster.
How did I get 3 ?
Here is the formula you can use : - >The ratio of rate of S vs all the Others combined will always be greater than (1-r)/r [r = 1/4 here]
How can you deduce that ?
Consider a GP : a, ar, ar^2, ar^3,.......to infinity
a/(ar+ar^2+ar^3+...to infinity) = a/[ar*(1+r+r^2+....to infinity)] = a/[ar*1/(1-r)] = (1-r)/r
Now here since the time taken 13:4 or 3.25:1, that means one group is 3.25 times faster than the others.
If S is the fastest, you have to select him to get you this ratio, So only choices : P,S and Q,S makes sense.
Since it is just a little more than 3, my gut feeling says, combine the fastest with the slowest as my my first choice (luckily that is true here).
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