Question

P,Q and R can do a piece of work in 18 days, 36 days and 54 day respectively. They start the work together but Q and R leave 1 day and 5 days respectively, before the completion of work. In how many days has the work been completed ?

A. 10
B. 11
C. 10 7/11
D. 10 9/11

Answer 1

P, Q, and R work together on a piece of work that is completed in 10 7/11 days. P works the full duration, but Q leaves one day early and R leaves five days early. The total work completed together is equivalent to 1 unit, leading to the equations solved for the duration x.

Step-by-step explanation:

To solve when the work has been completed by P, Q, and R, we need to find out how much work each does per day and then calculate based on the days they each worked before leaving.

P can do the work in 18 days, so P's work per day is 1/18. Q's work per day is 1/36, and R's work per day is 1/54. If we add these together, we get the work done per day when they all work together:

1/18 + 1/36 + 1/54=
1/12 (this is the total work done by all three per day).

Let the total number of days they worked together be x. Since Q leaves one day before and R leaves 5 days before completion, Q works for x-1 days and R works for x-5 days. P works for the full x days.

So, the equation becomes:
P's work + Q's work + R's work = 1, which represents the whole work.

(x/18) + ((x-1)/36) + ((x-5)/54) = 1

Now, let's solve for x:

After finding the common denominator and combining like terms, the equation simplifies to:

9x - 3(x - 1) - (x - 5) = 18

After expanding and combining like terms, we get:

9x - 3x + 3 - x + 5 = 18

5x + 8 = 18

Subtract 8 from both sides:

5x = 10

Divide by 5:

x = 10 7/11 days

Therefore, the work was completed in 10 7/11 days.