Question

A cistern can be filled by a tap in 4 hrs and another tap in 6 hours how long will it take to fill the cistern if both tap are opened together ?

Answer 1

$\underline{ \underline{ \mathfrak{Answer}}} : - \\ \implies \:\bf{cistern\: filled\: in \:12 \:hr } \\ \\ \mathfrak{ \underline{\underline{Step - by - step \: explanation}} }: - \\ \\ \underline{\underline{Given}} : - \\ \\ \bf{Time \: taken \: by \: first \: tap \: to \: fill \: it \: = 4 \: hr} \\ \\ \bf{in \: 1 \: hr \: part \: of \: cistern \: filled = \frac{1}{4} } \\ \bf{in \: 1 \: hr \: part \: of \: cistern \: emptied = \frac{1}{6} } \\ \\ if \: both \: tap \: are \: opened \: simultaneously \: \\ then \\ \\ in \: 1 \: hr \: part \: of \: cistern \: filled = \frac{1}{4} - \frac{1}{6} \\ \: \implies \: \frac{1}{12} \\ \\ \frac{1}{12} part \: can \: be \: filled \: in \: = 1 \: hr \\ \\ \bf{cistern \: filled \: in \:12 \: hr}$