Twenty men were employed to do some work in a certain time. It was found that, after one-third of the scheduled time, only one-quarter of the total work was completed. How many more men should now be employed to complete the work in 3/4th of the originally scheduled time

Sure, let's solve this step by step:

Step 1: Understand the problem The problem states that 20 men were employed to do some work in a certain time. After one-third of the time, only one-quarter of the work was completed. We need to find out how many more men should be employed to complete the work in 3/4th of the originally scheduled time.

Step 2: Set up the equation Let's denote the total work as W, the total time as T, and the number of men as M. According to the problem, we have the following relationships:

• 20 men can do 1/4 of the work in 1/3 of the time, so 20 * (1/3T) = 1/4W.
• We need to find out how many men (M) can do the remaining 3/4 of the work in the remaining 3/4 of the time, so M * (3/4T) = 3/4W.

Step 3: Solve the equation From the first equation, we can express W in terms of T: W = 20 * 3T = 60T. Substitute W into the second equation, we get M * (3/4T) = 3/4 * 60T. Simplify the equation, we get M = 60.

Step 4: Find out how many more men are needed Since originally there were 20 men, we need 60 - 20 = 40 more men to complete the work in 3/4th of the originally scheduled time.