# CAT Quantitative Aptitude Questions | CAT Time and Work questions

###### CAT Questions | Time and work | Work Time

The question is from Time and work: Three friends, combines with the idea of Algebra. The combination of the slowest two and the quickest two and the respective time to complete the task is given and we need to find out the time required by all three. x's and y's introduced into any topic can complicate anything, including pipes and cisterns. CAT Questions from Time and Work.

Question 6: Consider three friends A, B and C who work at differing speeds. When the slowest two work together they take n days to finish a task. When the quickest two work together they take m days to finish a task. One of them, if he worked alone would take thrice as much time as it would take when all three work together. How much time would it take if all three worked together?

1. $$frac{3mn}{2$m + n$}$ 2. $\frac{2mn}{m + n}\\$ 3. $\frac{4mn}{3$m + n$}$ 4. $\frac{5mn}{3$m + n$}$ ## 🎉🎉Special Independence day offer - get up to ₹ 10,000 off on our courses! #### Register Now ## Best CAT Online Coaching Try upto 40 hours for free Learn from the best! #### 2IIM : Best Online CAT Coaching. ### Video Explanation ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now! ### Explanatory Answer ##### Method of solving this CAT Question from Pipes Cisterns and Work Time: x's and y's introduced into any topic can complicate anything, including pipes and tanks. Let A < B < C in terms of efficiency. B and C together take n days. A and B together take m days. One of them, if he worked alone would take thrice as much time as it would take when all three work together. This is a crucial statement. Now, if there are three people who are all equally efficient, for each of them it would take thrice as much time as for all three together. Now, this tells us that the person who takes thrice as much time cannot be the quickest one. If the quickest one is only one-third as efficient as the entire team, the other two cannot add up to two-thirds. By a similar logic, the slowest one cannot be the person who is one-third as efficient. In other words, the person one-third as efficient = B Let A, B and C together take x days. B alone would take 3x days B and C together take n days. Or B + C in 1 day do $\frac{1}{n}\\$ of the task ........Eqn$i)
A and B together take m days. Or, A + B in 1 day do
$$frac{1}{m}\\$ of the task ........Eqn$ii)
B takes 3x days to do the task. Or, B, in one day, does
$$frac{1}{3x}\\$ of the task ........Eqn$iii)

Now, if we do (i) + (i) – (iii) we get
A + B + C do $$frac{1}{n}\\$ + $\frac{1}{m}\\$ - $\frac{1}{3x}\\$ in a day. This should be equal to $\frac{1}{x}\\$ as all three of them complete the task in x days. $\frac{1}{n}\\$ + $\frac{1}{m}\\$ - $\frac{1}{3x}\\$ = $\frac{1}{x}\\$ $\frac{1}{n}\\$ + $\frac{1}{m}\\$ = $\frac{4}{3x}\\$ $\frac{m + n}{mn}\\$ = $\frac{4}{3x}\\$ $\frac{4mn}{3$m + n$}$ The question is "How much time would it take if all three worked together?" ##### Hence, the answer is "$\frac{4mn}{3$m + n$}$". Choice C is the correct answer. ###### 🎉Special Independence day offer - get up to ₹ 10,000 off on our courses! ★ Register now ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2024 Classroom Batches Starting Now! @Gopalapuram and @Anna nagar ###### Best CAT Coaching in Chennai Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## CAT Online Coaching | CAT Arithmetic Videos On YouTube #### Other useful sources for Arithmetic Questions | Pipes Cisterns; Time and Work Sample Questions ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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