Question

Team members can complete a job in 20 days but with the help of their team leader, they can complete it in 15 days. In how many days can the team leader alone complete the job?

• A. 20 Days
• B. 40 Days
• C. 60 Days
• D. 80 Days

Answer 1

The Correct Option is C

Finding the Time Taken by the Team Leader Alone 

Step 1: Define the Total Work

Let the total work be \( W \) (in terms of work units).

Step 2: Work Rate of Team Members

The team members can complete the work in 20 days, so their rate of work is:

\[ \text{Rate of work of team members} = \frac{W}{20} \]

Step 3: Work Rate of Team Members with the Team Leader

With the help of their team leader, they can complete the work in 15 days. Hence, the combined rate of work is:

\[ \text{Combined rate of work} = \frac{W}{15} \]

Step 4: Find the Work Rate of the Team Leader

Let the rate of work of the team leader be \( x \). Then, we have the equation:

\[ \frac{W}{20} + x = \frac{W}{15} \]

Solving for \( x \):

\[ x = \frac{W}{15} - \frac{W}{20} \]

Taking LCM of 15 and 20, we get: \[ x = W \left(\frac{1}{15} - \frac{1}{20} \right) \]

\[ x = W \left(\frac{4}{60} - \frac{3}{60} \right) = W \times \frac{1}{60} \]

Step 5: Find the Time Taken by the Team Leader Alone

The team leader alone can complete the total work \( W \) at a rate of \( W/60 \) per day, so the total time required is:

\[ \frac{W}{W/60} = 60 \text{ days} \]

Final Answer:

Thus, the team leader alone can complete the job in 60 days. The correct answer is (C) 60 days.