Pipe A can fill a tank in 4 hours and pipe B that can fill a tank in 2 hours. Both are opened when   the tank is empty . Pipe A is closed 30 minutes before the tank overflows. How long did it take for the tank to overflow? Options :120 minutes90 minutes100 minutesnone

To solve this problem, we need to first understand the rate at which each pipe fills the tank.

Pipe A fills the tank in 4 hours, so it fills 1/4 of the tank in 1 hour. Pipe B fills the tank in 2 hours, so it fills 1/2 of the tank in 1 hour.

When both pipes are open, they fill the tank at a rate of 1/4 + 1/2 = 3/4 of the tank per hour.

We know that Pipe A is closed 30 minutes (or 0.5 hours) before the tank overflows. This means that for the last 0.5 hours, only Pipe B was open, filling the tank at a rate of 1/2 of the tank per hour.

So in the last 0.5 hours, Pipe B filled 0.5 * 1/2 = 1/4 of the tank.

This means that before Pipe A was closed, 3/4 of the tank was already filled.

We can now calculate how long it took both pipes to fill 3/4 of the tank.

If both pipes together fill the tank at a rate of 3/4 per hour, then it would take them 1 / (3/4) = 4/3 hours to fill 3/4 of the tank.

So, the total time it took for the tank to overflow is the time it took both pipes to fill 3/4 of the tank plus the time it took Pipe B to fill the last 1/4 of the tank.

This is 4/3 hours + 0.5 hours = 1.33 hours + 0.5 hours = 1.83 hours.

Converting this to minutes (since the options are given in minutes), we get 1.83 hours * 60 minutes/hour = 110 minutes.

So, the correct answer is none of the given options.