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. $$frac{2}{3}\\$ 2. $\frac{1}{6}\\$ 3. $\frac{1}{2}\\$ 4. $\frac{1}{3}\\$ Rs. 2500 off on 2IIM Ultimate DI LR Course for CAT 2019. Offer valid till March 24th. Signup to sample the Best CAT Online Coaching Best CAT Coaching in Chennai Starts Sat, Mar 23, 2019 Explanatory Answer Method of solving this CAT Question from Pipes Cisterns and Work Time: We can do trial and error to arrive at the answer! Let Amar take x days and Akbar take y days to finish the work. So, Anthony would take x-1 days to complete the work alone. Therefore, as per question, $\frac{1}{x}\\$ + $\frac{1}{$x-1$}$ + $\frac{1}{y}\\$ = 1 …………………$1)
Also given, ($$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. Online CAT CoachingTry it free! Register in 2 easy steps and start learning in 30 seconds! Already have an Account? CAT Coaching in Chennai Next Weekend Batch Starts Sat, Mar 23rd, 2019 Best CAT Coaching in Chennai Sign up for a Free Demo of our CAT Coaching in Chennai 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, 10-C, Kalinga Colony, Bobbili Raja Salai K.K.Nagar, Chennai. India. Pin - 600 078 How to reach 2IIM? Phone:$91) 44 4505 8484
Mobile: (91) 99626 48484
WhatsApp: WhatsApp Now
Email: prep@2iim.com