Solution
Given:In this question it is mentioned that
• Three printing presses A, B, and C, working together at their respective constant rates, take 2 hours to do a certain printing job.
• However, if only B and C are working, they can complete the same printing job in 4 hours.
To find: • The number of days A alone will take to complete the job
Approach and Working: As the job remains same, we can assume the total job to be the 12 units (multiple of the LCM of 2 and 4)
• A, B, and C together take 2 hours to complete 12 units of work
• Therefore, in 1 hour all of them will do \(\frac{12}{2}\) = 6 units of work
• B and C together take 4 hours to complete 12 units of work
• Therefore, in 1 hour they will do \(\frac{12}{4}\) = 3 units of work
Now, in 1-hour time, A, B, and C together do 6 units, out of which B and C do 3 units work
• Therefore, in 1 hour, A will do (6 – 3) = 3 units of work
So, working alone at this constant rate, A will take \(\frac{12}{3}\) days = 4 hours to complete the same job.
Hence, the correct answer is option C.
Answer: CImportant Observation
• As mentioned in the article, when we assume the total job to be the LCM of the given number of hours, the calculation becomes much easy as we can avoid fractional calculations. However, in this case we have assumed the total job to be a multiple of the LCM, which shows not only the LCM but any multiple of LCM value can give you the same answer.