# Rakesh does half of the work in 30 days and Sanny does remaining work in 7.5 days. In how many days the work will be completed by them if they work to

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Rakesh does half of the work in 30 days and Sanny does remaining work in 7.5 days. In how many days the work will be completed by them if they work together?

1. 12 days
2. 13 days
3. 15 days
4. 20 days
5. 14 days

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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