Verified answer

Answer:

[tex]\boxed{ \sf{ \:\bf \: Time \: taken \: to \: empty \: the \: cistern = 90 \: hours \: }}\\ \\ [/tex]

Step-by-step explanation:

Given that, a pipe can fill a cistern in 9 hours.

Let assume that Volume of cistern be V.

So,

[tex]\sf \: Amount \: of \: water \: in \: cistern \:in \: one \: hour = \dfrac{V}{9} \\ \\ [/tex]

Further given that, due to a leak in its bottom, the cistern fills up in 10 hours.

So,

[tex]\sf \: Amount \: of \: water \: in \: cistern \:in \: one \: hour = \dfrac{V}{10} \\ \\ [/tex]

Thus,

[tex]\sf \: Amount \: of \: water \: leak \:in \: one \: hour = \dfrac{V}{9} - \dfrac{V}{10} \\ \\ [/tex]

[tex]\sf \: Amount \: of \: water \: leak \:in \: one \: hour = \dfrac{10V - 9V}{90}\\ \\ [/tex]

[tex]\sf \: Amount \: of \: water \: leak \:in \: one \: hour = \dfrac{V}{90}\\ \\ [/tex]

So,

If the cistern is full, then time taken so that cistern will be empty by the leak is 90 hours.

Hence,

[tex]\bf\implies \: Time \: taken \: to \: empty \: the \: cistern = 90 \: hours\\ \\ [/tex]