Among the four people Sachin, Sourav, Yuvraj, and Dhoni, Sachin takes three times as long as Sourav to do a work. To complete the same work, Sourav takes three times as long as Yuvraj, and Yuvraj takes three times as long as Dhoni. A group of three out of four people can do the work in 13 days, while another group of three people can do the same work in 31 days. Which is the group that takes 13 days to complete the work?

Among the four people Sachin, Sourav, Yuvraj, and Dhoni, Sachin takes three times as long as Sourav to do a work. To complete the same work, Sourav takes three times as long as Yuvraj, and Yuvraj takes three times as long as Dhoni. A group of three out of four people can do the work in 13 days, while another group of three people can do the same work in 31 days. Which is the group that takes 13 days to complete the work? Correct Answer Sachin, Sourav and Dhoni

Given :

Sachin takes three times longer than Sourav to do a work 

To complete the same work, Sourav takes three times as long as Yuvraj

To complete the same work Yuvraj takes three times as long as Dhoni

Concept used :

Person's per day work = Total work/Number of days he takes to complete the work 

Calculations :

Let the time taken by Dhoni be 't'

The time taken by Yuvraj will be '3t' 

The time taken by Sourav will be '9t' 

The time taken by Sachin will be '27t'

Now, 

Total work = LCM of t, 3t, 9t, and 27t 

⇒ 27t units 

Sachin's per day work = 27t/27t = 1 unit

Sourav's per day work = 27t/9t = 3 units 

Yuvraj's per day work = 27t/9t = 9 units 

Dhoni's per day work = 27t/t = 27 units 

One group can complete the work in 13 days and another group can complete in 31 days so,

The efficiency of the 1st group : Efficiency of 2nd group = 1/13 : 1/31 

⇒ 31 : 13 

We can see here 

Efficiency (Dhoni, Sourav and Sachin) : Efficiency (Sachin, Sourav and Yuvraj) = 31 : 13 

∴ Dhoni, Saurav, and Sachin group can complete the work in 13 days