Abhay and Shreya can individually complete a piece of work in and respectively. Starting with Abhay, they work alternately for a minute each till the work is completed, with only the one working at the end being allowed to work for less than a minute in the final turn. How long will it take the duo to complete the work?
- A52 mins 24 secs
- B52 mins 30 secs
- C52 mins 36 secs
- D52 mins 40 secs
Solution & Step-by-step Explanation
Let the total work be the of and .
Now, find their efficiencies per minute:
Since they work alternately starting with Abhay:
* Minute 1 (Abhay):
* Minute 2 (Shreya):
Total work done in 1 cycle () .
To find the number of full cycles near :
Remaining work .
Now, it is Abhay's turn. Abhay's efficiency is .
Converting to seconds:
Total time taken .
Now, find their efficiencies per minute:
Since they work alternately starting with Abhay:
* Minute 1 (Abhay):
* Minute 2 (Shreya):
Total work done in 1 cycle () .
To find the number of full cycles near :
Remaining work .
Now, it is Abhay's turn. Abhay's efficiency is .
Converting to seconds:
Total time taken .