MAH MCA CET 2024
A and B can complete a work in 12 days, B and C complete a work in 15 days and C and A can complete a work in 20 days. Find in how many days they all together can complete a work?
Answer (Detailed Solution Below)View answer ▾Hide ▴
Answer: Option A — 10
Detailed Solution
One day's work: , , .
Adding all three: .
, so all three together take 10 days.
✓ Check
, , , and , as given.⚠ Common trap
Option (C), 12 days, is the time A and B take as a pair; adding C's work must make the time shorter than any pair's, so 12 is too long.Quick tip
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Time & Work — Preparation
This question tests your understanding of Time & Work, a key topic in the Quantitative Aptitude section. The detailed solution above uses a step-by-step approach to show the reasoning, and where available, a shortcut that helps you solve similar questions in under 90 seconds during the actual exam.
Time and work questions deal with how long one or more people, machines or pipes take to complete a task. The core idea is that if someone finishes a job in n days, they complete 1/n of the job each day. Questions involve people working together, joining or leaving partway, working on alternate days, efficiency comparisons, and wages shared in proportion to work done. Pipes and cisterns questions use the same logic and have their own page. The LCM method is the fastest approach for most questions. Take the total work as the LCM of the individual times, find each person's work per day, and the rest becomes simple division. This avoids messy fractions and makes problems with three or more workers much easier to handle. Practise the time and work questions below. Each solution shows the step-by-step working and the LCM shortcut where it helps.