Robert Bosch Pipes and Cistern Quiz-3

Solution:
Given, time taken by a tap to completely fill the cistern = 4 hours
Therefore, time taken a tap to fill the cistern half = 2 hours (4/2)
Cistern filled by three pipes in 1 hour = 3*1/4 = 3/4 hours.
Therefore, remaining part = 1-1/2 = 1/2
= 3/4 : 1/2 = 1 : x
x = 2/3 = 40 minutes.
Hence, total time taken = 2 hours and 40 minutes.

Solution:
Let the capacity of tanks be 180 units( LCM of 36 and 60)
Efficiency of tap A = 5 units/mins
Efficiency of tap B = 3 units/mins
1/6th of tank = 30 units
Required time = 30/5+3 = 15/4 mins

Solution:
Given A can fill in 16 mins
B can fill in x mins
C can empty in 12 mins
and A, B and C together = 240/7
A/c to the question,
1/16 + 1/x+ 1/12 = 7/240
1/x = 1/20
X = 20 mins

Solution:
Given, X takes 20 minutes
Given, Y takes 25 minutes
Tank filled in 5 minutes = 1/20 + 1/25 = 9/20
Therefore, remaining part = 11/20
Tank filled by Y in 1 minute = 1/25
Therefore, 1/25 : 11/20 :: 1: a
a = 11/20 * 1 * 25 = 55/4
Therefore, 55/4 = 13 minutes and 45 seconds.
Hence, the tank will take 18 minutes and 45 seconds to fill completely.

Solution:
Part filled by pipes (A + B + C) in 10 minutes
= 10 (1/60 +1/50+1/30) = 21/30
Water filled by pipe A in 10 minutes = 10 * 1/60 = 1/6
Therefore, the required ratio = 1/6 * 30/21 = 5/21

Capacity of tank= LCM of 6 and 9= 36 units
Total efficiency of A and B= 36/6 = 6 units/h

Total efficiency of Band C = 36/9 = 4 units/h
Let the efficiency of A, B and C be x, y and z units/h.
Then, 4(x+y) + 1 (y + z) + 5 x z=36 ⇒ z = 1.6

Time taken by C alone to fill the whole tank = 36/1.6

= 22.5 h

Solution:
Let the pipe R alone can empty the tank in x minutes
A/c to question,
20 [ 1/24 + 1/30 - 1/x] = 1
X = 40 mins
Capacity of tank= 8*40*½ = 160 gallons

Solution: Water tank filled in 8 hours = 1/7

Now, due to outlet pipe, 1 hour part filled = 1/6

Part of the water tank unfilled in 1 hour = 1/6 - 1/7 = 1/42

So, the leak will empty the full water tank in 42 hrs

Solution: Portion filled by pipes (A + B + C) in 4 minutes = 4 (1/30 +1/15+1/25) = 42/75

Salt water filled by pipe R in 4 minutes = 4 * 1/25 = 4/25

Therefore, the required ratio = 4/25 * 42/75 = 168/1875

Correct option is : A

Solution:

(1/x)-(1/28) = -(1/42)

(1/x) = (1/28)-(1/42)

(1/x)= 84 min

Capacity of the tank = 84 *2.5 =210 liters