in Quantitative Aptitude retagged by
588 views
1 vote
1 vote
Amar, Akbar and Anthony are working on a project. Working together Amar and Akbar can complete the project in $1 \; \text{year},$ Akbar and Anthony can complete in $16$ months, Anthony and Amar can complete in $2 \; \text{years}.$ If the person who is neither the faster nor the slowest works alone, the time in months he will take to complete the project is
in Quantitative Aptitude retagged by
2.7k points
588 views

1 Answer

1 vote
1 vote

Let’s draw the diagram for a better understanding.

$\begin{array}{llll} & \textbf{Amar + Akbar} & \textbf{Akbar + Anthony} & \textbf{Anthony + Amar} \\\hline \text{Time :} & 12\;\text{months} &  16\;\text{months} & 24\;\text{months} \\ \text{Total work :} & \text{LCM(12,16,24)} & = & 48\;\text{units} \\ \text{Efficiency :} & 4\;\text{units/month} & 3\;\text{units/month}  & 2\;\text{units/month}   \end{array}$

Let the efficiency of Amar, Akbar, and Anthony be $x, y$, and $z\;\text{units/month}.$

Now, $x+y+y+z+z+x = 4+3+2$

$\Rightarrow 2(x+y+z) = 9$

$\Rightarrow \boxed{x+y+z = 4.5}$

Now, we can calculate the individual efficiency.

  • The efficiency of Amar $x = 4.5-3 = 1.5$
  • The efficiency of Akbar $y = 4.5-2 = 2.5$
  • The efficiency of Anthony $z = 4.5-4 = 0.5$

We can say that Anthony is the slowest, Akbar is the fastest.

$\therefore$ The Person who is neither the fastest nor the slowest (Amar) works alone, the time is taken by him to complete the project $= \frac{48\; \text{units}}{1.5\;\text{units/month}} = 32\; \text{months}.$

Correct Answer $: 32$

edited by
10.3k points
Answer:

Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true