Question

Two pipes P and Q would fill an empty cistern in 24 minutes and 32 minutes respectively. Both the pipe being opened together,find when the first pipe must be turned off so that the empty cistern may be filled in 16 minute IN DIRECT AND INVERSE VARIATION QUESTION

Answer 1

Pipe P can fill a cistern in 24 minutes
So in 1 minute, P fills : 1/24 part of the tank [Time proportional to Work, when the time decreases, the amount of work also decreases]

Pipe Q can fill the cistern in 32 minutes
So in 1 minute, Q fills : 1/32 part of the tank.

The cistern has to be filled in 16 minutes. [we have to find when the first pipe should be closed so that cistern is full in 16 minutes.]
So Pipe Q is open for the whole time, 16 minutes.
In 16 minutes Pipe Q fills : 16 * 1/32 = 1/2 part of the tank.
Remaining part = 1 - 1/2 = 1/2 part.
This has to be filled by pipe P
1 min == 1/24 part
X mins == 1/2 part
X/24 = 1/2
X = 24/2 = 12 minutes.

Hence pipe P has to be closed after 12 minutes, so that the cistern will be full in 16 minutes.
[pipe P and Q works for 12 minutes, then for the next 4 minutes pipe Q alone works]
Hope it helps.