Question

00. An inlet pipe and outlet pipe are taking turns to fill and drain a cistern, respectively, for an hour each at a time, starting with the inlet pipe when the cistern is empty. It takes the inlet pipe 15 hours to fully fill the empty cistern, whereas the outlet pipe can drain the filled cistern completely in 21 hours. How many hours will it take for the cistern to be full? (a) 100 (b) 52.5 (c) 105 (d) 99 ​

Answer 1

Answer:

kya hogya teko???

bta de yaar kyu ni bol ra mere se

Answer 2

Answer:

Inlet pipe can fill a cistern in = 15 hours

∴ In 1 hour the inlet pipe can fill = 1/15

Outlet pipe can empty a cistern in = 21 hours

∴ In 1 hour the outlet pipe can empty = 1/21

In 1st our cistern is filled = 1/159

In the next every 2 hours cistern is filled = (1/15 - 1/21) = 2/105

Let, the cistern will be filled in next 2x hours

According to the question,

⇒ 1/15 + 2x/105 = 1

⇒ 2x/105 = 1 - 1/15

⇒ 2x = 14/15 × 105

⇒ 2x = 98

∴ It will take (1 + 98) = 99 hours to fill the cistern

Alternate Method Sunny 28.7.21

LCM of 15 and 21 is 105

⇒ The capacity of the cistern is 105

In 1 hour Inlet can fill 105/15 = 7 unit

In 1 hour outlet can empty 105/21 = 5 unit

As, both pipes are open in an alternate hour, in 2 hour cistern will fill by (7 - 5) = 2 unit

After filling the cistern, the outlet will not count

In the last one hour inlet will fill 7 unit

Remaining (105 - 7) = 98 units

To fill 98 units required time = 2 × (98/2) hours [∵ In 2 hours fill 2 unit]

⇒ 98 hours

Total required time = (98 + 1) = 99 hours

∴ It will take 99 hours to make the cistern full.