# CAT Quantitative Aptitude Questions | CAT Time and Work questions

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

The question is from Time and Work. Here, work is getting interrupted by continuous kidnapping, Still, the work gets done :).

Question 24: Amar, Akbar and Anthony set out to complete a work. Anthony being the eldest would take 1 day less than Amar if he were to complete the work alone. All three together could complete the work in a day. However, Anthony was kidnapped by Shakal. Amar and Akbar began the work in his absence. After a day, Amar was also kidnapped. Akbar took 3 more days to finish the work. How much portion of the work Anthony could do in a day?

1. $$frac{2}{3}\\$ 2. $\frac{1}{6}\\$ 3. $\frac{1}{2}\\$ 4. $\frac{1}{3}\\$ ## Nail CAT 2020 with Test Dojo2,500 off on Dojo and Part courses. Signup Now! #### 2IIM : Best Online CAT Coaching. ## Best CAT Coaching in Chennai #### CAT Coaching in Chennai - CAT 2020Online Batches Available Now! ### Explanatory Answer ##### Method of solving this CAT Question from Pipes Cisterns and Work Time: We can do trial and error to arrive at the answer! Let Amar take x days and Akbar take y days to finish the work. So, Anthony would take x-1 days to complete the work alone. Therefore, as per question, $\frac{1}{x}\\$ + $\frac{1}{$x-1$}$ + $\frac{1}{y}\\$ = 1 …………………$1)
Also given, ($$frac{1}{x}\\$ + $\frac{1}{y}\\$ + $\frac{3}{y}\\$) = 1 => $\frac{1}{x}\\$ + $\frac{4}{y}\\$ = 1 =>$$$frac{1}{y}\\$ = $\frac{1}{4}\\$ + $\frac{1}{4x}\\$ = 1 ………………………$2)
Putting in equation (1),
=> $$frac{1}{x}\\$ + $\frac{1}{$x-1$}$ + $\frac{1}{4}\\$ - $\frac{1}{4x}\\$ = 1 => $\frac{1}{x}\\$ + $\frac{1}{$x-1$}$ - $\frac{1}{4x}\\$ = $\frac{3}{4}\\$ Now using option analysis, a) Work done by Anthony in 1 day = $\frac{1}{$x-1$}$ = $\frac{2}{3}\\$ =) 3 = 2x - 2 =) x = $\frac{5}{2}\\$ = 2.5 L.H.S of$3) => $$frac{1}{2.5}\\$ + $\frac{1}{1.5}\\$ - $\frac{1}{10}\\$ = 0.4 + 0.66 – 0.1 ≠ 0.75 b) $\frac{1}{$x-1$}$ = $\frac{1}{6}\\$ =) x = 7 L.H.S of$3) = $$frac{1}{7}\\$ + $\frac{1}{6}\\$ - $\frac{1}{28}\\$ ≠ $\frac{3}{4}\\$ c) $\frac{1}{$x-1$}$ = $\frac{1}{2}\\$ =) x = 3 L.H.S of$3) = $$frac{1}{3}\\$ + $\frac{1}{2}\\$ - $\frac{1}{12}\\$ = $\frac{$4 + 6 – 1$}{12}$ = $\frac{9}{12}\\$ = $\frac{3}{4}\\$ The question is "How much portion of the work Anthony could do in a day?" ##### Hence, the answer is "$\frac{1}{2}\\$". Choice C is the correct answer. ###### Nail CAT 2020 with 2IIM. 2,500 Off on Test Dojo and Part courses. Signup Now ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2020Enroll at 30,000/- Online Classroom Batches Starting Now! ###### Best CAT Coaching in ChennaiPrices slashed by Rs 5000/- Attend a Demo Class ## 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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