Robert Bosch Pipes and Cisterns Quiz-1

Answer: option b

Explanation:
If a pipe requires 'x' hrs to fill up the tank, then part filled in 1 hr=1/x
If pipe A requires 12 hrs to fill the tank, then part filled by pipe A in 1 hr = 1/12

If pipe B requires 36 hrs to fill the tank, then part filled by pipe B 1 hr = 1/36

Hence, part filled by (A + B) together in 1 hr = 1/12 + 1/36

= 48 / 432 = 1/9

In 1 hr both pipes together fill 1/9th part of the tank. This means, together they fill the tank in 9 hrs.

Answer: option b

Explanation: Assume the total time required = x + 2 min
Part filled by pipe A in 1min = 1/5 & part filled by B in 1 min = 1/10
After 2 min, part filed by A & B together = 2 [ 1/5 + 1/10] = 3/5

Remaining part = 1 – 3/5 = 2/5
Part filled by pipe B in 1 min = 1/10

As pipe A is turned off after 2 minutes, we get the relation as,

Part filled by(A+B)in 1hr / Remaining part :: Total part filled/Time taken

1/10 : 2/5 :: 1: x

x = (2/5) x 1 x 10 = 4 min

Tank will be full in ( 2 min + 4 min) = 6 min

Answer: option c

Explanation: Assume that the tank will be full in '10 + x' hrs.

Part filled by pipe A in 1 hr = 1/15
Part filled by pipe B in 1 hr = 1/20
Part emptied by pipe C in 1 hr = 1/ 25

(A+ B)'s part filled in 1 hr = 1/15 + 1/20 = 7 /60

As Pipe C is closed after 10 hours, let us find the part of tank filled in 10 hrs.
Tank filled in 10 hrs = 10 (part filled by A in 1 hr + part filled by B in 1 hr– part emptied by C in 1 hr)
= 10 [1/15 + 1/20 – 1/25] = 23 /30

Remaining part = 1 – part filled in 10 hours
= 1 – 23/30 = 7/30

We know that,
Part filled by(A+B)in 1hr / Remaining part :: Total part filled/Time taken

So, we get the ratio as ,

7/60 : 7/30 :: 1 : x

So, the value of x = 2/30 x 1 x 60/7 = 2 hrs.

Hence, the tank will be full in x + 2 = 10 + 2 hrs = 12 hrs

Answer: option b

Explanation: Pipe A's work in 1 hr = 1/8
Pipe B's work in 1 hr = 1/6

Pipes (A+B)'s work in first 2 hrs when they are opened alternately = 1/8 + 1/6 = 7 /24

Now,

In 4 hrs they fill : 2 X (7/24) = 7/12
In 6 hrs they fill : 3 X (7/24) = 7/8

After 6 hrs, part left empty = 1/8

Now it is A's turn to open up.

In one hr it fills 1/8 of the tank.

So, the tank will be full in = 6 hrs + 1 hr = 7 hrs

Answer: option d

Explanation: Assume that the reservoir is filled by first pipe in 'x' hours.
So, the reservoir is filled by second pipe in 'x + 20' hours.
Now, from these above conditions, we can form the equations as,

1/x + 1/ (x + 20) = 1/24

[x + 20 + x] / [x(x + 20)] = 1/24

x2 – 28x – 480 = 0

By solving this quadratic equation , we get the factors (x – 40) (x+12) = 0
Hence, we get two values : x = 40 & x = -6
Since filling of reservoir is positive work , we can neglect the negative value of 'x'.
Thus, x = 40

This means that the second pipe will take (x+ 20) hrs = 40 + 20 = 60 hrs to fill the reservoir.

Answer: option d

Explanation: Consider a pipe fills the tank in 'x' hrs. If there is a leakage in the bottom, the tank is filled in 'y' hrs.
The time taken by the leak to empty the full tank =xy/(y-x) hrs

Time taken to empty the tank by the leak = 4 x (9/2) / (9/2 ) - 4 = (36/2 ) / 1/2 = 18/ 1/2 = 18 x 2 = 36 hrs

Answer: option d

Explanation: Work done by waste pipe in 1 min = (Part filled by total pipes together) -(part filled by first pipe + part filled by second pipe)
= 1/6 – [(1/10) + (1/14)] = 1/6 – (24/140) = -1/210
Here, negative (-) sign indicates emptying of tank.

To find the capacity, we need to determine the volume of 1/210 part.
Therefore, volume of 1/210 part = 4 gallons ---------(given condition)
Hence, the capacity of tank = volume of whole = 4 x 210 = 840 gallons.

Explanation:Let B be turned off after x minutes. Then,
Part filled by (A + B) in x min. + Part filled by A in (30 - x) min. = 1
Therefore, x(2/75 + 1/45) + (30 - x) = 2/75 = 1
=> 11x/225 + (60 - 2x)/75 = 1
=> 11x + 180 - 6x = 225
=> x = 9
So 9 mins is the answer.

Answer: option C

Explanation: Net part filled in 1 hour (1 / 5 + 1 / 6 - 1 / 12)
= 17 / 60

Therefore, the tank will be full in 60 / 17 hours
i.e., 3 9/17 hrs

Answer: option d

Explanation: 1/8 - 1/x = 1/10
1/8 -1/10=1/x
5/40-4/40=1/x
1/40=1/x
x = 40