Piyush can complete 60% of a work in 3 days while Bipin can complete (3/4)th part of the same work in 6 days. In how many days (13/8) part of the work will be completed if both of them work together?

Option 3 : 5 days

Given:

Number of days taken by Piyush to complete 60% of a work = 3 days.

Number of days taken by Bipin to complete (3/4)th part of a work = 6 days.

Concept Used:

Work Efficiency: Work Efficiency essentially means the rate of work, i.e. the amount of work done in unit time.

The more time one takes to complete a job, the less efficient the person is. Similarly, the less time one takes to complete a job, the more efficient the person is.

Therefore, we can say that efficiency is inversely proportional to the time taken to complete the work.

**Formula Used:**

Work Efficiency = Work Done/Time taken

**Calculation:**

Work efficiency of Piyush = Work Done/Time taken

⇒ {(60/100)/3}

⇒ 60/300 = 1/5

Work efficiency of Bipin = Work Done/Time taken

⇒ {(3/4)/6}

⇒ 3/24 = 1/8

Now, Combined Efficiency = Work efficiency of Piyush + Work efficiency of Bipin

⇒ (1/5) + (1/8) = (8 + 5)/40 = 13/40

So, Time taken by Piyush and Bipin together to complete (13/8) part of the work = (Work Done)/(Combined Efficiency)

⇒ (13/8)/(13/40)

⇒ 40/8 = 5 days

**∴ Piyush and Bipin will complete (13/8) part of the work by working together in 5 days.**

__Alternate Method__

Piyush can complete 60% of work in 3 days

⇒ Piyush can complete the whole work in 3 × (100/60) = 5 days

Bipin can complete 3/4 work in 6 days

⇒ Bipin can complete the whole work in 6/(3/4) = 8 days

Together they can complete the work in 40/(8 + 5) = 40/13 days

Time taken to complete 13/8 part of work = (13/8) × (40/13) = 5 days

∴ Piyush and Bipin will complete (13/8) part of the work by working together in 5 days.