Bodhee Prep-CAT Online Preparation

CAT 2021 Quant Question [Slot 1] with Solution 17

Question
Amar, Akbar and Anthony are working on a project. Working together Amar and Akbar can complete the project in 1 year, Akbar and Anthony can complete in 16 months, Anthony and Amar can complete in 2 years. If the person who is neither the fastest nor the slowest works alone, the time in months he will take to complete the project is
Option: 32
Solution:
Let the total work be 48 units. Let Amar do 'm' work, Akbar do 'k' work, and Anthony do 'n' units of work in a month.
Amar and Akbar complete the project in 12 months. Hence, in a month they do \(\frac{{48}}{{12}}\)=4 units of work.
m+k = 4.
Similarly, k+n = 3, and m+n = 2.
Solving the three equations, we get \(m = \frac{3}{2},\;k = \frac{5}{2},\;n = \frac{1}{2}\).
Here, Amar works neither the fastest not the slowest, and he does 1.5 units of work in a month. Hence, to complete the work, he would take \(\frac{{48}}{{1.5}} = 32\) months.
CAT Online Course @ INR 9999 only

CAT 2021 Quant questions with Solutions

CAT 2023
Classroom Course

We are starting classroom course for CAT 2023 in Gurugram from the month of December.
Please fill the form to book your seat for FREE Demo Classes

CAT 2023 Classroom Course starts in Gurgaon