Pipe A can fill a tank in 16 minutes and pipe B cam empty it in 24 minutes. If both the pipes are opened together after how many minutes should pipe B be closed, so that the tank is filled in 30 minutes ?

Correct Answer: 50 cub.m/min

Explanation:

Let filling capacity of the pump be 'F' m 3 / min

Then, the filling capacity of the pump will be (F + 10) m 3 / min

From the given data,

$$\begin{gathered} 2400 F - 2400 F + 10 = 8 \\ ? 2400 F + 10 - F F ( F + 10 ) = 8 \\ ? F 2 + 10 F - 3000 = 0 \\ ? F = 50 m 3 / min \end{gathered}$$

Correct Answer: 24min

Explanation:

Given taps X and Y can fill the tank in 30 and 40 minutes respectively. Therefore,

 

part filled by tap X in 1 minute = 1/30

 

part filled by tap Y in 1 minute = 1/40

 

Tap Z can empty the tank in 60 minutes. Therefore,

 

part emptied by tap Z in 1 minute = 1/60

 

Net part filled by Pipes X,Y,Z together in 1 minute = [1/30 +1/40 - 1/60] = 5/120 = 1/24

 

i.e., the tank can be filled in 24 minutes.

 

 

Correct Answer: 11 days 7 hours

Correct Answer: 30 min

Explanation:

Part filled by (A + B) in 1 minute = (1/60 + 1/40) = 1/24
Suppose the tank is filled in x minutes.
Then, x/2(1/24 + 1/40) = 1
(x/2) * (1/15) = 1 => x = 30 min.

Correct Answer: 170 lit

Explanation:

Given A alone can fill the tank of capacity 240 lit in 16 hrs.

=> A can fill in 1 hr = 240/16 = 15 lit

=> B alone can fill the tank of capacity 240 lit in 12 hrs.

=> B can fill in 1 hr = 240/12 = 20 lit

Now, (A + B) in 1 hr = 15 + 20 = 35 lit

But they are opened for 2 hrs

=> 2 x 35 = 70 lit rae filled

Remaining water to be filled in tank of 240 lit = 240 - 70 = 170 lit.

Correct Answer: 12 min

Explanation:

Let the efficiencies of filling pipes is 4p and 5p respectively.

Efficiency of pipe which empty the tank = 2/3 x 9p/2 = 3p

Total work = 3p x 36 = 108p

 

Time to fill the tank by both the pipes = 108p/9p = 12 min.

Correct Answer: 3 hrs 45 min

Explanation:

Time taken by one tap to fill half of the tank = 3 hrs.

Part filled by the taps in 1 hour = 4 x 1/6 = 2/3

Remaining part = 1 - 1/2 = 1/2

2/3 : 1/2 :: 1 : p

p = 1/2 x 1 x 3/2 = 3/4 hrs. i.e., 45 min

So, total time taken = 3 hrs 45 min.

Correct Answer: 12 min

Explanation:

Let pipe A takes p min to fill

Then,

pipe B takes 3p min to fill

=> 3p - p = 32

=> p = 16 min => 3p = 48 min

 

Required, both pipes to fill = (48 x 16)/(48 + 16) min = 12 min.

Correct Answer: 40 hrs

Explanation:

The time taken by the leak to empty the tank =  1 8 - 1 10 = 5 - 4 40 = 1 40

Therefore, the leak empties the tank in 40 hours.

Correct Answer: 26.166 minutes

Explanation:

Upto first 5 minutes I, J and K will fill => 5[(1/20)+(1/30)+(1/40)] = 65/120

For next 6 minutes, J and K will fill => 6[(1/30)+(1/40)] = 42/120

So tank filled upto first 11 minutes = (65/120) + (42/120) = 107/120
So remaining tank = 13/120

Now at the moment filling with C and leakage @ 1/60 per minute= (1/40) - (1/70) = 3/280.
So time taken to fill remaining 13/120 tank =(13/120) /(3/280) = 91/6 minutes

 

Hence total time taken to completely fill the tank = 5 + 6 + 91/6 = 26.16 minutes.