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Two taps $A$ and $B$ can fill a tank in $12$ minutes and $15$ minutes respectively. The tank can be emptied by a third tap $C$ in $6$ minutes. If $A$ and $B$ are kept open for $5$ minutes in the beginning and then $C$ is opened along with $A$ and $B$ being kept open, the time taken to empty the tank is:

  1. $60$ minutes
  2. $45$ minutes
  3. $30$ minutes
  4. $75$ minutes
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Given that, $A\quad B \quad C$

Time $:\quad 12\quad 15\quad 6\quad$ minues

Total tank capacity $:LCM(12,15,6) = 60$ litre

Efficiency $: 5 \quad 4 \quad -10\quad $ litre/minute

Tap $A$ and $B$ open for $5$ minutes, then they can fill $5 \times 9 = 45$ litre

Now, all three taps are open, then the time taken to empty the tank is  $\dfrac{45}{1} = 45$ minutes.

So, the correct answer is $(B).$
Answer:

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