Dear Reader,
Below are four problems dealing with time calculations on pipes and cistern.
Question 1
Two pipes X and Y together can fill a tank in 72 minutes. If the size of the pipe X is thrice as Y then Y alone can fill the tank in:
a) 5 hours and 12 minutes
b) 3 hours and 56 minutes
c) 4 hours and 48 minutes
d) none of these
Answer : c) 4 hours and 48 minutes.
Solution :
Let the time taken by Y alone to fill the tank be A minutes.
Given that, the size of the pipe X is thrice as Y.
Then, X fills the tank in A/3 minutes.
Part filled by X in 1 minute = 1/(A/3) = 3/A
Part filled by Y in 1 minute = 1/A.
Since, X and Y together take 72 minutes.
Part filled by (X+Y) in 1 minute = 1/72
i.e., (1/A + 3/A) = 1/72
4/A = 1/72
A = 288 minutes = 288/60 hours = 4 + 48/60 = 4 + 4/5 hours
= 4 hours and 4/5 x 60 minutes = 4 hours and 48 minutes.
Hence, the pipe Y alone takes 4 hours and 48 minutes to fill the tank.
Question 2
Pipe X can fill a cistern thrice as fast as another pipe Y and the pipe Y is thrice as fast as pipe Z. If X, Y and Z together fill the cistern in 10 minutes then the time taken by X to fill the cistern is:
a) 1 hour and 42 minutes
b) 2 hours and 10 minutes
c) 1 hour and 23 minutes
d) none of these
Answer : b) 2 hours and 10 minutes
Solution :
Let the pipe Z alone takes A minutes to fill the tank.
Given that, Y is thrice as fast as Z.
Then, Y takes A/3 minutes to fill the tank.
And, X is thrice as fast as Y.
X takes (A/3)/3 = A/9 minutes to fill the tank.
Now,
Part filled by X in 1 minute = 9/A
Part filled by Y in 1 minute = 3/A
Part filled by Z in 1 minute = 1/A
Net part filled by (X+Y+Z) in 1 minute = 9/A + 3/A + 1/A = 13/A
(X+Y+Z) take 10 minutes to fill the cistern.
Part filled by (X+Y+Z) in 1 minute = 1/10
Thus, we have, 1/10 = 13/A
A = 130
Therefore, Z alone takes 130 minutes i.e., 2 hours and 10 minutes.
Question 3
Pipe X takes 6 hours to fill a cistern and another pipe Y takes 7 and half hours to fill the same cistern. If the pipes X and Y are switched together at the same time and X is closed after 1 and half hours then the extra time taken by Y to fill the cistern is:
a) 39/8 hours b) 41/8 hours c) 37/8 hours d) none of these.
Answer : a) 39/8 hours
Solution :
X takes 6 hours, part filled by X in 1 hour = 1/6
Y takes 7 and half hours, part filled by Y in 1 hour = 1/7.5 or 2/15.
Therefore, the part filled by X and Y together = 1/6 + 2/15
X and Y together fill the cistern for 1 and half hour i.e., 3/2 hours.
Part filled by (X+Y) in 3/2 hours = (3/2)(1/6 + 1/15) = (3/2)(7/30) = 7/20
Remaining part filled by Y alone = 1 - 7/20 = 13/20.
Below are four problems dealing with time calculations on pipes and cistern.
Question 1
Two pipes X and Y together can fill a tank in 72 minutes. If the size of the pipe X is thrice as Y then Y alone can fill the tank in:
a) 5 hours and 12 minutes
b) 3 hours and 56 minutes
c) 4 hours and 48 minutes
d) none of these
Answer : c) 4 hours and 48 minutes.
Solution :
Let the time taken by Y alone to fill the tank be A minutes.
Given that, the size of the pipe X is thrice as Y.
Then, X fills the tank in A/3 minutes.
Part filled by X in 1 minute = 1/(A/3) = 3/A
Part filled by Y in 1 minute = 1/A.
Since, X and Y together take 72 minutes.
Part filled by (X+Y) in 1 minute = 1/72
i.e., (1/A + 3/A) = 1/72
4/A = 1/72
A = 288 minutes = 288/60 hours = 4 + 48/60 = 4 + 4/5 hours
= 4 hours and 4/5 x 60 minutes = 4 hours and 48 minutes.
Hence, the pipe Y alone takes 4 hours and 48 minutes to fill the tank.
Question 2
Pipe X can fill a cistern thrice as fast as another pipe Y and the pipe Y is thrice as fast as pipe Z. If X, Y and Z together fill the cistern in 10 minutes then the time taken by X to fill the cistern is:
a) 1 hour and 42 minutes
b) 2 hours and 10 minutes
c) 1 hour and 23 minutes
d) none of these
Answer : b) 2 hours and 10 minutes
Solution :
Let the pipe Z alone takes A minutes to fill the tank.
Given that, Y is thrice as fast as Z.
Then, Y takes A/3 minutes to fill the tank.
And, X is thrice as fast as Y.
X takes (A/3)/3 = A/9 minutes to fill the tank.
Now,
Part filled by X in 1 minute = 9/A
Part filled by Y in 1 minute = 3/A
Part filled by Z in 1 minute = 1/A
Net part filled by (X+Y+Z) in 1 minute = 9/A + 3/A + 1/A = 13/A
(X+Y+Z) take 10 minutes to fill the cistern.
Part filled by (X+Y+Z) in 1 minute = 1/10
Thus, we have, 1/10 = 13/A
A = 130
Therefore, Z alone takes 130 minutes i.e., 2 hours and 10 minutes.
Question 3
Pipe X takes 6 hours to fill a cistern and another pipe Y takes 7 and half hours to fill the same cistern. If the pipes X and Y are switched together at the same time and X is closed after 1 and half hours then the extra time taken by Y to fill the cistern is:
a) 39/8 hours b) 41/8 hours c) 37/8 hours d) none of these.
Answer : a) 39/8 hours
Solution :
X takes 6 hours, part filled by X in 1 hour = 1/6
Y takes 7 and half hours, part filled by Y in 1 hour = 1/7.5 or 2/15.
Therefore, the part filled by X and Y together = 1/6 + 2/15
X and Y together fill the cistern for 1 and half hour i.e., 3/2 hours.
Part filled by (X+Y) in 3/2 hours = (3/2)(1/6 + 1/15) = (3/2)(7/30) = 7/20
Remaining part filled by Y alone = 1 - 7/20 = 13/20.
Part Filled Time Taken by Y 2/15 1 hour 13/20 ?Time taken to fill 13/20 part by Y alone = 13/20 x 15/2 = 39/8 hours.
