Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 3 minutes the first is…

8 1/4 min





NA

Solution :

P takes 12minutes to fill the cistern. So, in 1 minute it can fill,

=> 1/12 part of the cistern

Q takes 15 minutes to fill the cistern. So, in 1 minute it can fill,

=> 1/15 part of the cistern

The two pipes can together fill,

=> 1/12 + 1/15 = 9/60 = 3/20 part of the cistern in 1 minute.

So, in 3 minutes they fill,

=> (3/20)(3)

= 9/20

Remaining part of the cistern which needs to be filled = 1 - (9/20)

= 11/20

If Q fills 1/15 part of the cistern in 1 minute then 11/20 part of the cistern can be filled in,

=> [1/(1/15)] × (11/20)

=> 15 × (11/20)

=> 33/4

= 8 (1/4) minutes

So, the correct option is 8 (1/4) minutes.