A can lay railway track between two given stations in 22 days and B can do the same job in 11 days. With the help of C, they did the job in 5 days only. Then, C alone can do the job in

Correct option is A

Given:

A completes the work in 22 days, B in 11 days, and together with C they finish in 5 days.

Formula Used:
Work rate =$$\dfrac{1}{\text{time}}.$$​​
Time =$$\dfrac{1}{\text{rate}}.$$​​

Solution:
A’s rate =$$\dfrac{1}{22}$$​, B’s rate =$$\dfrac{1}{11}=\dfrac{2}{22}.$$​​
(A + B) rate =$$\dfrac{3}{22}$$​.
Given (A + B + C) rate =$$\dfrac{1}{5}.$$​​

So, C’s rate =$$\dfrac{1}{5}-\dfrac{3}{22}=\dfrac{22-15}{110}=\dfrac{7}{110}$$​ (work/day).

C alone takes $$=\dfrac{1}{\frac{7}{110}}=\dfrac{110}{7}$$ days $$=15\frac{5}{7}$$​ days.

Alternate Method :
Assume total work =LCM(22,11,5) = 110 units.
A does $$\frac{110}{22}=$$​5 units/day, B does $$\frac{110}{11}$$​=10 units/day.
Together with C they finish in 5 days $$= \frac{110}5=2$$​2 units/day.
Hence C’s rate = 22 - (5 + 10) =7 units/day

time =$$\frac{110}7$$​days = $$=15\frac{5}{7}$$​days.