P and Q do a project in 150 days and 100 days respecively. In how many days can they complete 60% of the project if they work together.

Options

A. a. 12days
B. b. 72days
C. c. 42days
D. d. 36days

Answer

To solve the problem, we need to determine how many days P and Q will take to complete 60% of a project when they work together. Here’s a step-by-step solution:

### Step 1: Determine the total work done by P and Q
- Let’s assume the total work of the project is represented by a common multiple of the days they take to complete the project.
- P completes the project in 150 days, and Q completes it in 100 days.
- The least common multiple (LCM) of 150 and 100 is 300. Thus, we can consider the total work to be 300 units.

### Step 2: Calculate the work done per day by P and Q
- Work done by P in one day = Total work / Days taken by P = 300 / 150 = 2 units per day.
- Work done by Q in one day = Total work / Days taken by Q = 300 / 100 = 3 units per day.

### Step 3: Calculate the combined work done by P and Q in one day
- Total work done by both P and Q in one day = Work done by P + Work done by Q = 2 + 3 = 5 units per day.

### Step 4: Calculate 60% of the total work
- 60% of the total work = 60/100 * 300 = 180 units.

### Step 5: Calculate the number of days required to complete 60% of the work
- To find out how many days it will take for P and Q to complete 180 units of work, we divide the total work (180 units) by the combined work done in one day (5 units).
- Days required = Total work to be done / Work done in one day = 180 / 5 = 36 days.

### Conclusion
P and Q can complete 60% of the project in **36 days** when they work together.