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Three pipes $\text{A, B}$ and $\text{C}$ can fill a cistern in $8$ minutes, $12$ minutes and $16$ minutes respectively. What is the time taken by three pipes to fill the cistern when they are opened together?

  1. $3.7$ minutes
  2. $6$ minutes
  3. $4.5$ minutes
  4. $5$ minutes
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In 8 minute A fill 1 unit volume of the cistern

In 1 minute A fill  $\frac{1}{8}$ unit volume of the cistern


In 12 minute B fill 1 unit volume of the cistern

In 1 minute B fill  $\frac{1}{12}$ unit volume of the cistern


In 16 minute C fill 1 unit volume of the cistern

In 1 minute C fill  $\frac{1}{16}$ unit volume of the cistern

so if all the three pipes A,B,C open together then in 1 minute it can fill ,

$\frac{1}{8}+\frac{1}{12}+\frac{1}{16}$ part of the cistern

so, A,B,C together $\frac{13}{48}$ unit cistern in 1 minute

so to fill the 1 unit total it will take time $\frac{48}{13}$ minute =3.7 minute

so correct answer is 3.7 minutes.(A)

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