Question

Acistern is filled in 5 hours and it takes 6 hours when thereis a leak in its bottom. If the cistern is full, in what time shall the leak empty it?

• A. 6 hrs
• B. 5 hrs
• C. 30 hrs
• D. 15 hrs

Answer 1

The Correct Option is C

For the capacity of cistern Take LCM of 5,6 = 30

Efficiency to fill the cistern = \(\frac{30}{5}\) \(\frac{units}{hr}\)

= 6 \(\frac{units}{hr}\)

Assume the efficiency of leak = \(- x \frac{units}{hr}\)

From the question, \((6 - x) × 6 = 30\)

\(6 - x = 5\)

\(x = 1 \)

From above, time taken by leak to empty it = \(\frac{30}{1} hrs\) 

The correct option is (C): 30 hrs