a) 22\large\frac{1}{2} hours

b) 16\large\frac{1}{2} hours

c) 12\large\frac{1}{2} hours

d) 10\large\frac{1}{2} hours

correct answer is:

a) 22\large\frac{1}{2} hours

Explanation

Here,
Pumps are inversely proportional to Hours.
Water is directly proportional to Hours.
\therefore x=18\times\large\frac{10}{14}\normalsize\times\large\frac{31500}{180000}
\rightarrow x=\large\frac{315}{14}
\rightarrow x=22\large\frac{1}{2} hours
Ans: To irrigate 315000 litres of water, a 14 H.P. pump should be operated for 22\large\frac{1}{2} hours.