Correct answer is: b) 14 days

Explanation

Bighas and Days are Directly Proportional.
Hours and Days are Inversely Proportional.
So that,
18\;:\;21\;\&\;10\;:\;15\;:\;:\;8\;:\;x
\rightarrow\large\frac{18\times10}{21\times15}=\frac{8}{x}
\rightarrow\large\frac{4}{7}=\frac{8}{x}
\rightarrow 4x=56
\rightarrow x=\large\frac{56}{4}
\rightarrow x=14
\therefore 14 days will it take to irrigate 21 bighas of land by operating the pump 10 hours per day.
Ans: Working 21 bighas 10 hours per day the tube will take 14 days to complete the work.

These particular questions can also be asked in the following ways:

1. Suppose a shallow tube-well pump working 15 hours per day can irrigate 18 bighas of land in 8 days. How many days will it take to irrigate 21 bighas of land by operating the pump for 10 hours per day?
2. If a shallow tube-well pump can irrigate 18 bighas of land in 8 days by working 15 hours per day, how many days will it take to irrigate 21 bighas of land by operating the pump for 10 hours per day?
3. How many days are needed to irrigate 21 bighas of land by operating a shallow tube-well pump for 10 hours per day, if the pump can irrigate 18 bighas of land in 8 days working 15 hours per day?