A cistern can be filled by two pipes a and b in 10 and 15 hours respectively and is then empited by a tap in 8 hours.If all the taps are opened,then cistern will be fill in
Answers
Answer:
A cistern can be filled by two pipes a and b in 10 and 15 hours respectively and is then empited by a tap in 8 hours.If all the taps are opened,then cistern will be filled in 24 hours
Step-by-step explanation:
Find the fraction that all the taps opened together will fill in an our:
Tap a fills the cistern in 10 hours:
If 10 hours = 1/1 of the cistern
Then 1 hour = 1 ×1/10
Tap a fills a tenth , 1/10 of the cistern in 1 hour
Tap b can fill the cistern is 15 hours:
If 15 hours = full cistern, 1
Then 1 hour = 1 × 1/15
Tap b in 1 hour fills 1/15 of the cistern
Tap C can empty the tank in 8 hours:
If 8 hours = 1
Then 1 hour = 1 × 1/8
Therefore tap c empties 1/8 of the cistern in 1 hour
⇒ Add tap a and b and minus c to find the fraction of the tap that will be filled in an hour:
a + b - c = 1/10 + 1/15 - 1/8
= (12 + 8 - 15) / 120
= 5 / 120
= 1 / 24
Therefore the fraction of the cistern filled when all 3 taps are opened in an hour is 1 / 24 .
Find the time it will take the whole cistern to be filled if in 1 hour the fraction filled is 1/24
If 1/24 of the cistern = 1 hour
Then 24/24 of the cistern = 1 hour × 24/24 ×24/1
= 24 hours
Therefore if the three taps are opened the cistern will be full after 24 hours.