HSBC Pipes and Cistern Questions and Answers Quiz-1

Explanation: Let pipe M fills the cistern in x minutes.
Therefore, pipe N will fill the cistern in (x+5) minutes.
Now, 1/x + 1/(x+5) = 1/6 → x = 10
Thus, the pipe M can fill in 10 minutes, so N can fill in 10+5 =15 minutes.

Explanation: As cistern is filled in 10 hours, therefore in 1 hour, filled part → 1/10th
Now, due to outlet pipe, filled part in 1 hour = 1/15th
Part of the cistern emptied, due to leakage in 1 hour = 1/10 - 1/15 = 1/30th
Therefore the leak will empty the full cistern in 30 hrs.

Explanation: Cistern filled by both pipes in one hour = 1/12+1/20=2/15th
Therefore both pipes filled the cistern in 15/2hrs.
Now, due to leakage both pipes filled the cistern in 15/2+30/60=8hrs.
Therefore Due to leakage, filled part in one hour = 1/8
Therefore part of cistern emptied, due to leakage in one hour = 2/15-1/8= 1/120th
∴ In 120 hrs, the leak would empty the cistern.

Explanation: P can fill the cistern in 36 minutes,so in 1 min, P can fill the cistern = 1/36th part
In 24 min, P can fill the cistern = 24/36 = 2/3rd. Remaining part = 1- 2/3 = 1/3rd
As Q can fill full cistern in 48 minutes,so it will fill
1/3rd part in 16 minutes.

Explanation: Let the required time be x hours, then
⇒ x/16+3x/80 = 1⇒ x= 11=10 hours.

Explanation: Let M was turned off after x min. Then, cistern filled by M in x min + cistern
filled by N in (x+5) min = 1 ⇒ x/30 + (x+5)/20 = 1 ⇒ 5x+15=60 ⇒ x = 9 min.

Explanation: Let cistern will be full in x min. Then part filled by A in x min + part filled by
B in (x-2) min + part filled by C in (x-4) min = 1
⇒ x/12 + (x-2)/16 + (x-4)/20 = 1 ⇒ 47x - 78 = 240⇒ x = 162/47 = 321/47 min

Explanation: Suppose pipe A alone takes x hours to fill the tank.
Then pipes B and C will take x/3 and x/6 hours respectively to fill the tank.
Therefore 1/x + 3/x + 6/x= 1/20 ⇒ 10/x = 1/20 ⇒ x = 200hrs

Explanation: (P+Q)’s 1 hour’s work = (1/10+1/20) = 3/20
(A+C)’s 1 hour’s work = (1/10+1/30) = 2/15
Part filled in 2 hrs = (3/20+2/15) = 17/60
Part filled in 6 hrs = (3×17/60) = 17/20
Remaining Part = (1-17/20) = 3/20
Now, it is the turn of P and Q and 3/20 part is filled by P and Q in 1 hour.
Therefore, Total time taken to fill the tank = (6+1) hrs = 7 hrs

Explanation: Let speed of the bike be x km/hr. Let speed of the electric car be y km/hr
∴ 200/x + 600/y = 10 ∴ 300/x + 500/y = 11
Part filled in 1 hour
= (1/10-1/12) = 1/60
Time taken to fill the tank = 60 hours
Water filled in 60 hours =4*60*60=1440 litres