A can lay railway track between two given stations in 17 days and B can do the same job in 16 days. With the help of C, they did the job in 4 days only. Then, C alone can do the job in

A’s rate = $\frac{1}{17}$ work/day
B’s rate = $\frac{1}{16}$ work/day

Together with C, work is completed in 4 days:
Total rate = $\frac{1}{4}$ work/day

So,
$\frac{1}{17} + \frac{1}{16} + \text{C’s rate} = \frac{1}{4}$

LCM of 17 and 16 = 272

$\frac{1}{17} = \frac{16}{272}, \quad \frac{1}{16} = \frac{17}{272}$

So,
$\frac{16}{272} + \frac{17}{272} = \frac{33}{272}$

C’s rate:
$\frac{1}{4} - \frac{33}{272}$

$\frac{1}{4} = \frac{68}{272}$

C’s rate = $\frac{68 - 33}{272} = \frac{35}{272}$

Time taken by C alone:
$\frac{1}{\frac{35}{272}} = \frac{272}{35} = 7 \frac{27}{35}$ days

Correct Answer: $7 \frac{27}{35}$ days