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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**

3 Answers 3

0

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.

  • 0
    If any doubt please ask. – 2017-02-10
  • 0
    I got 2.75 after adding 11.am what i will get – 2017-02-10
  • 0
    I mentioned your mistake. – 2017-02-10
  • 0
    ok Thank you so Much @Kanwalijit singh – 2017-02-10
  • 0
    Mine pleasure :-) – 2017-02-10
2

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.

  • 0
    No the Answer is 2.40 am – 2017-02-10
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    The answer is wrong. Or the question is. – 2017-02-10
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    No its correct answer. – 2017-02-10
  • 0
    Then the question is wrong. – 2017-02-10
  • 0
    That comment is incomprehensible. – 2017-02-10
  • 0
    Okay, that was a mistake. – 2017-02-10
  • 0
    what i am doing mistake, while i am trying – 2017-02-10
  • 0
    See my answer. Its correct. – 2017-02-10
  • 0
    Your method is also correct. Only mistake is in first step. Your calculation is wrong. – 2017-02-10
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    At least I deserve thanks from you. Otherwise you are making correct question and correct answer are wrong. – 2017-02-10
1

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