Karan works twice as fast as Shyam. Working together, they can complete a task in 20 days. In how many days will Karan alone complete the same task?

Karan works twice as fast as Shyam.

Together, they can complete the task in 20 days. 

Concept Used: ​

Efficiency (E) is inversely proportional to the time time taken (T).

i.e.  $$E \propto \frac{1}{T}$$         

As given in the question;

Karan Efficiency = 2 times Shyam efficiency  

​$$\frac{K_E}{S_E} = \frac{2}{1}$$      

​$$\frac{K_T}{S_T} = \frac{1}{2}$$       

Now. Total work = $$\text{Efficiency}\times \text{time}$$ 

total work = $$20 \times 3 = 60 unit$$ 

Now, time taken by Karan alone to complete the work 

= $$\frac{60}{2} = 30 days$$ ​