1. A tank is usually filled in 18 hours. But because of a leak in its bottom, it takes another 6 hours to fill. How much time will be taken by the leak to empty the full tank ?

A. 30 hours B. 72 hours C. 42 hours D. 55 hours

Answer Answer: Option B Explanation: Consider the case when there is no leak . Then in one hour, work done = 1/18, and in 6 hours = 6/18 = 1/3.
This means 1/3rd of the tank is emptied because of the leakage in 18 + 6 = 24 hours
So, 1/3rd is emptied in 24 hours, full tank would be emptied in 24 × 3 = 72 hours.

2. Pipes A and B can fill a tank in 5 & 6 hrs respectively.Pipe C can empty it in 12 hrs.If all the 3 pipes are opened together,then the tank will be filled in?

A. 1 13/17 hrs B. 2 8/11 hrs C. 3 9/17 hrs D. 4 1/2 hrs

Answer Answer: Option C Explanation: Net part filled in 1 hr = (1/5+1/6 - 1/12) = 17/60.
Therefore the tank will be full in 60/17 hrs i.e. 3 9/17 hrs.

3. The volume of water flowing through a pipe is directly proportional to square of its radius. A tank has four inlet pipes with diameters as 2 cm, 4 cm, 6 cm and 8 cm. if the smallest pipe, alone, can fill a tank in 30 hours, then how much time would all the four pipes, when working together would take ?

A. 1 hours B. 4 hours C. 6 hours D. None of these

Answer Answer: Option A Explanation: We are given that V = k (r2) where V is volume of water and ‘r’ is radius of pipe and k is a constant.
The smallest pipe takes 30 hours to fill the tank alone, hence work done in 1 hour = 1/30
Radius = diameter / 2 = 2/2 = 1
1/30 = k (12), so k = 1/30
Work done in 1 hour by pipe 2 = 1/30 (4/2)2 = 4/30
Work done in 1 hour by pipe 3 = 1/30 (6/2)2 = 9/30
Work done in 1 hour by pipe 4 = 1/30 (8/2)2 = 16/30
In 1 hour, work done by all the four pipes = (1/30) + (4/30) + (9/30) + (16/30) = 30 / 30 = 1
Hence, the whole tank gets filled in 1 hour.

4. 3 pipes A, B & C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is?

A. 10 B. 12 C. 14 D. 16

Answer Answer: Option C Explanation: Part filled in 2 hours = 2/6 = 1/3, Remaining part = (1- 1/3) = 2/3.
Therefore (A+B)'s 7 hours work = 2/3: (A+B)'s 1 hour's work =2/21.
Therefore C's 1 hour's work = {(A+B+C)'s 1 hour's work - (A+B)'s 1 hour's work}
=(1/6-2/21)=1/14
Therefore C alone can fill the tank in 14 hours.
t

5. A pipe can fill a tank in 4 hours. But due to a leak in the tank, it is filled in 5 hours. If the tank is full. How much time will the leak to empty the tank completely ?

A. 10 hours B. 15 hours C. 20 hours D. 12 hours

Answer Answer: Option C Explanation: In 1 hour., water filled = 1/4 th of the tank.
1/4 th is emptied by leakage in 5 hours
Full tank would be emptied in 20 hours (or)
[using formula, t = (5 × 4) / (5-4) = 20 hours]