Question

Pipes A, B and C can fill a tank in 30, 60 and 120 minutes respectively. Pipes B and C are kept open for 10 minutes, and then Pipe B is shut while Pipe A is opened. Pipe C is closed 10 minutes before the tank overflows. How long does it take to fill the tank?
40 minutes
28 minutes
30 minutes
36 minutes

Answer 1

Explanation:

Assume that the tank has capacity of 120L.

1. 4 L per min
2. 2 L per min
3. 1 L per min

Part 1

B and C are kept open for 10 mins filling 3 x 10 = 30 L

90 L remaining to fill.

Part 2

B is shut and A is open

This means A and C are filling tank together (5L/min)

We dont know how long A an D are open

Part 3

C is closed 10 min before thank is overflowed

It means for last 10 mins only A is working which fill 40L at last.

Therefore in part 1 30L was filled and in part 3 40L was filled so remaining balance is 50L that should have been filled in part 2

So entire time taken is

10 + 10 + 10 = 30mins

Answer 2

Answer:

Hence it will take $30 \:minutes$ to fill the tank.

Step-by-step explanation:

Let the total capacity of the tank be 120 liters.

As per the given data pipe A,B and C,

can fill the tank in $30$, $60$ and $120$ minutes respectively.
Step 1 :
The per minute work of -
pipe $A$ is = $\frac{120}{30} = 4$ liters per minute
pipe $B$ is = $\frac{120}{60} = 2$ liters per minute

pipe $C$ is = $\frac{120}{120} = 1$ liters per minute
Step 2:
Then according to the Question Pipe $B$ and $C$ are opened for $10$ minutes. Thus the total volume filled by them is = $(2+1)*10 = 30$ liters.
Then pipe $B$ is shut and Pipe $A$ is opened along with C.

We suppose that they run for $x$ minutes.

So total amount of volume filled by then = $(1+4)*x = 5x$ liters.
Then Pipe $C$ is shut and $A$ is allowed to run for last $10$ minutes.

So total volume filled by it is = $4*10=40$ liters.
Step 3:
Total volume of the tank is = $120 = 5x+40+30$
From here we get the value of $x$ as $10$ minutes.
Hence total time taken to fill the tank is = $10+10+10 = 30$ minutes