# Difficult Time and Work Solved QuestionAptitude Discussion

 Q. Among four persons Prince, Queen, Raj and Sashi. Prince takes thrice as much time as Queen to complete a piece of work. Queen takes thrice as much time as Raj and Raj takes thrice as much time as Sashi to complete the same work. One group of three of the four men can complete the work in 13 days while another group of three can do so in 31 days. Which is the group that takes 13 days?
 ✖ A. Prince, Queen, Raj ✔ B. Prince, Queen, Sashi ✖ C. Queen, Raj, Sashi ✖ D. Prince, Raj, Sashi

Solution:
Option(B) is correct

From the given information $Q$ is thrice as efficient as $P$.

$R$ is thrice as efficient as $Q$.

$S$ is thrice efficient as $R$.

If work done by $P$ in a day is '$n$' units, the work done in a day by $Q$, $R$ and $S$ would be $3n$, $9n$ and $27n$ units respectively.

It can be seem that, $P$, $Q$ and $R$ working together can do $13n$ units in a day while $P$, $Q$ and $S$ working together can do $31n$ units in a day.

Hence, the ratio of times taken to complete the work by the former and later groups is $31:13$
P, Q and S take 13 days.

## (3) Comment(s)

Swathi
()

if you go by work pqr=13/27 work and pqs = 31/27 work

ratio of work pqr:pqs = 13/27:31/27

therefore ratio of time pqr:pqs =27/13:27/31

=1/13:1/31 cross multiply it becomes 31:13 thus answer is pqs

Robot
()

by this logic P, Q and R would take 13 days i guess.

Sahib
()

Can anyone explain this concept, I did it by taking the number of days instead of taking work in a day. Acc. to question, P would take $27$ times the time S takes, Q would take $9$ times as compared to s, and R woud take $3$ times as compared to S. The answer coming is Q, R, S.