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 **