Vinayak and Nitin, working separately can do a piece of work in 8 and

1.	Vinayak and Nitin, working separately can do a piece of work in 8 and 12 hours respectively. If they work in stretches of one hour alternately, Vinayak beginning at 9 a.m., at what time the work be completed?1. 5:30 pm2. 9 pm3. 6:30 pm4. 7:30 pm
Answer» Correct Answer - Option 3 : 6:30 pm Given: Vinayak and Nitin, working separately can do a piece of work in 8 and 12 hours respectively. Calculations: Time taken by Vinayak to complete the work = 8 hours Part of the work done by Vinayak in 1 day = 1/8 similarly, Part of the work done by Nitin in 1 day = 1/12 Part of the work done by Vinayak and Nitin in the first 2 hours = (1/8) + (1/12) = 5/24 Part of the work done in first 8 hours = (5 × 4)/24 = 5/6 Remaining work = 1 - 5/6 = 1/6 Now, it is the turn of Vinayak, part of the work done by Vinayak in 1 hour = 1/8 Remaining work = (1/6) - (1/8) = 1/24 Now, time taken by Nitin in completing this part of the work = 12/24 = 1/2 hours Total time = 9 and 1/2 hours The work starts at 9 am. Hence, the work will be completed at 6.30 pm. ∴ the correct answer is 6:30 pm.

Vinayak and Nitin, working separately can do a piece of work in 8 and 12 hours respectively. If they work in stretches of one hour alternately, Vinayak beginning at 9 a.m., at what time the work be completed?1. 5:30 pm2. 9 pm3. 6:30 pm4. 7:30 pm

Answer» Correct Answer - Option 3 : 6:30 pm

Given:

Vinayak and Nitin, working separately can do a piece of work in 8 and 12 hours respectively.

Calculations:

Time taken by Vinayak to complete the work = 8 hours

Part of the work done by Vinayak in 1 day = 1/8

similarly, Part of the work done by Nitin in 1 day = 1/12

Part of the work done by Vinayak and Nitin in the first 2 hours = (1/8) + (1/12) = 5/24

Part of the work done in first 8 hours = (5 × 4)/24 = 5/6

Remaining work = 1 - 5/6 = 1/6

Now, it is the turn of Vinayak, part of the work done by Vinayak in 1 hour = 1/8

Remaining work = (1/6) - (1/8) = 1/24

Now, time taken by Nitin in completing this part of the work = 12/24 = 1/2 hours

Total time = 9 and 1/2 hours

The work starts at 9 am. Hence, the work will be completed at 6.30 pm.

∴ the correct answer is 6:30 pm.