A can lay a railway track between two given stations in 8 days and B can do the same job in 24 days. With the help of C, they can do the job in 3 days. C alone can do the job in:

Correct option is C

Given:

A completes the job in 8 days, B in 24 days, and (A + B + C) together in 3 days.

Find C’s time alone.

Formula Used:
Work rate $$= \frac{1}{\text{time}} .$$​​
Solution:

A’s rate $$= \frac{1}{8}$$​, B’s rate =$$\frac{1}{24}$$​​

A + B rate =$$\frac{1}{8} + \frac{1}{24} = \frac{1}{6}$$​.

(A + B + C) rate = $$\frac{1}{3}$$​​
So,

$$\frac{1}{6} + \frac{1}{C} = \frac{1}{3} \\ \ \\\frac{1}{C} = \frac{1}{3} - \frac{1}{6} = \frac{1}{6}$$​​
Hence C = 6 days.

Alternate Method—
Assume total work = LCM(8,24) = 24 units.
In 1 day: A does 3 units, B does 1 unit.
Together with C they finish in 3 days → per day = 24/3 = 8 units.
Thus C per day = 8 - (3 + 1) = 4 units

time = 24/4 = 6 days.