Vijay can do a piece of work in 4 hours. Ajay can do it in 28 hours. With the assistance of Amit, they completed the work in 3 hours. In how many hours can Amit alone do it?

Correct option is C

Given:

Vijay's time = 4 hours

Ajay's time = 28 hours

Combined time of Vijay, Ajay, and Amit = 3 hours

Formula Used:

Rate of person = $$\frac{1}{\text{Time taken by person}}$$​​

Solution:

Vijay's rate =$$\frac{1}{4}$$​​

Ajay's rate = $$\frac{1}{28}$$​​

Let Amit's rate be $$\frac{1}{x}$$​​

Now, 

​$$\frac{1}{4} + \frac{1}{28} + \frac{1}{x} = \frac{1}{3}$$​​

​$$\frac{7}{28} + \frac{1}{28} + \frac{1}{x} = \frac{1}{3}$$​​

​$$\frac{8}{28} + \frac{1}{x} = \frac{1}{3}$$​​

​$$\frac{2}{7} + \frac{1}{x} = \frac{1}{3}$$​​

​$$\frac{1}{x} = \frac{1}{3} - \frac{2}{7}$$​​

​$$\frac{1}{x} = \frac{7 - 6}{21} = \frac{1}{21}$$​​

x = 21

Therefore, Amit alone can do the work in 21 hours.

Alternate Solution:

Work = Efficiency × Time

Let total work = LCM(4, 28, 3) = 84 units

Vijay's efficiency = $$\frac{84}{4}$$​ = 21 units/hour

Ajay's efficiency =$$\frac{84}{28}$$​ = 3 unit/hour

Combined efficiency  = $$\frac{84}{3}$$​ = 28  hours

Amit’s efficiency = 28 - ( 21 + 3) = 4 

Amit's time = $$\frac{84}{4}$$​ = 21 hours