Pipe X that can fill a tank in an hour and pipe Y that can fill the tank in half an hour are opened simultaneously when the tank is empty. Pipe Y is shut 15 minutes before the tank overflows. When will the tank overflow?
Choices.
A) 35 mins  B) 30 mins  C) 40 mins  D) 32 mins  E) 36 mins

Rationale: the last 15 minutes only pipe x was open . since it needs 1 hour to fill the tank , then in 15 minutes it fills 1 / 4 th of the tank , thus 3 / 4 of the tank is filled with both pipes open . the combined rate of two pipes is 1 + 2 = 3 tanks / hour , therefore to fill 3 / 4 th of the tank they need ( time ) = ( work ) / ( rate ) = ( 3 / 4 ) / 3 = 1 / 4 hours = 15 minutes . total time = 15 + 15 = 30 minutes . answer : b
Answer: B