-2

Below is a sample time/work problem.

Rakesh alone can do a work in 10 days. Brijesh can do the same job in 15 days. If both Rakesh and Brijesh work together, then in how many days the work will get completed?

Above problem can be solved using LCM of $10$ and $15$.

Solution: Let $E$ denotes the efficiency. LCM($10, 15) = 30,E_R = 30/10 = 3, E_B = 30/15 = 2$

So each day both can complete $(3+2)$ units of the work, so they will take $30 / (3+2) = 6$ days to complete the whole work.

I wanted to know what is intuition behind taking the LCM of days as equivalent to the work units to be completed? How is it correct to consider LCM as total work units?

xrfxlp
  • 1,505
Akash
  • 3

1 Answers1

0

I prefer to think of the problem as follows:

Rakesh can do $\frac{1}{10}$ of a job in a day, while Brijesh can accomplish $\frac{1}{15}$ of a job in a day.

Together they can do $\frac{1}{10}+\frac{1}{15}=\frac{3}{30}+\frac{2}{30}=\frac{5}{30}=\frac{1}{6}$ of a job in a day.

Thus it will take 6 days to complete the job working together!

user3911635
  • 21
  • i know the above method, i just want to know how the LCM method works. It seems more easy than the fractions method. – Akash Jun 15 '19 at 04:00
  • [Edited solution to show an additional step]. As you can see the methods are equivalent. – user3911635 Jun 15 '19 at 04:03