Correct Answer - Option 1 : 12 days
Given:
Rakesh does half of a work in 30 days
Remaining work done by Sanny = (1 – 1/2)
⇒ (2 – 1)/2
⇒ 1/2 of the work in 7.5 days
Concept used:
If a person does a work in ‘n’ days, then one day work will be 1/n part of total work.
Total time taken for one work = the number of days/part of the work
Calculation:
One work done by Rakesh = 30/(1/2)
⇒ 60 days
Then one day work by Rakesh = 1/60 part of total work
One work done by Sanny = 7.5/(1/2)
⇒ 15 days
Then one day work by Sanny = 1/15 part of total work
Now, the one day work by Rakesh and Sanny = one day work by Rakesh + one day work by Sanny
⇒ 1/60 + 1/15
⇒ (1 + 4)/60
⇒ 5/60
⇒ 1/12
Then, time taken to complete one work by both Rakesh and Sanny = 12 days
∴ The work done by both when work together in 12 days