Question

Arjun and Bhasker can complete a task in 16 days working together. Bhasker alone can do it in 20 days. After working for 8 days, Bhasker left the task. How many days will Arjun take to complete the remaining tasks?
1. 40
2. 32
3. 16
4. 8

Answer 1

Correct Answer - Option 1 : 40

Given:

Time taken by Arjun and Bhaskar to complete the task = 16 days

Time taken by Bhaskar to complete the task = 20 days

Concept Used:

Total Work is LCM of time taken by all the persons.

Formula Used:

Total work = Efficiency × Time

Calculations:

Let efficiency of Arjun and Bhaskar be a and b respectively.

Total Work is LCM of time taken by all the persons.

⇒ Total work = LCM of (16, 20) = 80

Time taken by Arjun and Bhaskar to complete the task = 16 days

Total work = Efficiency × Time

80 = (a + b) × 16

⇒ a + b = 5      ----(1)

Time taken by Bhaskar to complete the task = 20 days

⇒ 80 = b × 20

⇒ b = 4      ----(2)

From (1) and (2), 

a = 5 – 4 = 1

Now, Bhaskar leaves after working for 8 days and Arjun completes the work

⇒ b × 8 + a × Time = 80

⇒ 4 × 8 + 1 × Time = 80

⇒ Time = 80 – 32

⇒ Time = 48 days

Time Taken by Arjun to complete the remaining task = 48 - 8 = 40

∴ The time Arjun takes to complete the remaining tasks is 40 days.