A cistern can be filled by two taps A and B in 12 hours and 16 hours respectively. The full cistern can be emptied by a third tap C in 8 hours. If all the taps are turned on at the same time, in how much time will the empty cistern be filled completely?
Answers
Answer:
Therefore, the Cistern will be filled up completely in 48 hours, if all the three taps are opened at the same time.
Step-by-step explanation:
Given that:- A cistern can be filled by two taps A and B in 12 hours and 16 hours respectively The full cistern can be emptied by a third tap C in 8 hours.
To find out:- If all the taps areturned on at the same time, in how much time will the empty cistern be filled up completely?
Solution:-
The time taken by A to fill the cistern = 12 hours
The time taken by B to fill the Cistern = 16 hours
The time taken by C to fill the Cistern = 8 hours.
Now, we have to find their first hour work,
∴ A's 1 hour's work = 1/12
B's 1 hour's work = 1/16
C's 1 hour's work = -1/8
∴ (ABC)'s 1 hour's work = (1/12)+(1/16)-(1/8)
LCM of 12,16 and 8 is 48.
= (3+4-6)/84
= (7-6)/48
= 1/48
Therefore, the Cistern will be filled up completely in 48 hours, if all the three taps are opened at the same time.
:)