Pipes and Cisterns: Two Pipe can fill a tank with water in 15 and 12 hrs respectively and a third pipe can empty it in 4 hrs .If the Pipe be opened in order at 8.am,9.am and 11.am respectively,the tank will be fully emptied at
I have tried:
8.am -9.am - 1/15
9.am - 10.am - 2/15 + 1/12
10.am -11.am -  3/15 + 2/12
before 11.am the tank will be filled - 3/15 + 2/12 -66/180 -22/60 = 11/30
after 11.am - 12.am three pipes are opened 1/15 + 1/12 - 1/4 = 1/10
The tank will be  at 12.am
11/30 -1/10 = 4/15
tank will  be fully emptied at - 15/4 = 3.75
after 12.am i am adding 12 + 3.75 - 2.75 pm
but the answer is 2.40,

What i am doing Mistake please anyone guide me for the Answer**

 A: With all pipes open the tank drains at a rate of $\frac 1 {15}+\frac 1 {12}-\frac 14=\frac {4+5-15}{60}=-\frac 1{10}$.
At 11 am the tank has filled $3*\frac 1 {15} +2*\frac 1 {12} =\frac 15+\frac 16=\frac {11}{30} $
So the tank will be empty in $\frac {11}{30}/\frac {1}{10}=\frac {11}3=3\frac 23$ hours = $3$ hours and $40$ minutes.  So it will be empty at $2:40$ pm.
A: 8 am to 9 am = $1$ hour, $1/15$ th of the tank filled
9 am to 11 am = $2$ hours, $(2*1/15 +2*1/12)$ of the tank filled
11 am to x am/pm = $a$ hours, $[(a*1/15+a*1/12)-(a*1/4)]$ filled
addition of all the above mentioned quantities should be zero if tank is completely emptied, $1$ if it is completely filled
so, $$\frac{1}{15}+2\cdot\frac{1}{15}+2\cdot\frac{1}{12}+a\cdot\frac{1}{15}+a\cdot\frac{1}{12}-a\cdot \frac{1}{4}=0$$
$a=220$, that is $3$ hours and $40$ mins after $11$ am
A: Your method has some mistake. After subtracting $\frac 1{10}$ for the first time. You are directly finding time.
It should be -
Tank at 1 p.m -
$\frac {4}{15} - \frac 1{10} = \frac 5{30}$
Tank at 2 p.m -
$\frac {5}{30} - \frac 1{10} = \frac 2{30} = \frac 1{15}$
After 2 p.m -
Fraction left $\frac {1}{15}$
Part is emptied in 1 minute $\frac {1}{600}$
$\frac {1}{15}$ part will be emptied in -
$\frac {1}{15} × 600$ = 40 minutes.
So tank is empty at 2:40 p.m

Alternative way -

I always used one shortcut.
$$\frac{\text{Part to be empty or filled}}{\text{Pipes working together}} $$
So we have,
$$= \frac{\frac {11}{30}}{\frac {1}{10}}$$
$= \frac {11}{30} × 10 = \frac {11}3$
$= \frac {11}3 × 60$
= 220 minutes or 3 hours 40 minutes.
