Question

A bottle is full of Dettol one third of it is taken out and then equal amount of water is poured in to the bottle to fill it, this operation is done four times. Find the final ratio of Dettol and water in the bottle.
$
  {\text{A}}{\text{. 13:55}} \\
  {\text{B}}{\text{. 20:74}} \\
  {\text{C}}{\text{. 16:65}} \\
  {\text{D}}{\text{. 10:48}} \\
$

Answer 1

Hint: To solve this first we have to assume the total amount of Dettol in the bottle is x liter and then subtract one third of it and note down the remaining Dettol and add one third of water and do the same simple mathematics four times to reach the final answer.

Complete step-by-step answer:
Let the beginning of the operation bottle have x liter of Dettol.

First operation:
$\dfrac{1}{3}$ part is taken out. So we have now in the bottle is,
$\dfrac{2}{3}x$ liter Dettol is remaining in the bottle and $\dfrac{1}{3}x$ liter water.
Second operation:
$\dfrac{1}{3}$ part of mixture is taken out. so we have now in the bottle is,
$\dfrac{2}{3}x - \dfrac{1}{3}\left( {\dfrac{2}{3}x} \right) = \dfrac{4}{9}x$liter of Dettol will be remaining in bottle,
Water present in bottle will be $\dfrac{1}{3}x - \dfrac{1}{3}\left( {\dfrac{1}{3}x} \right) + \dfrac{1}{3}x = \dfrac{5}{9}x$ liter water.
Third operation:
Again $\dfrac{1}{3}$ part of mixture is taken out. So we have now remaining in the bottle is
$\dfrac{4}{9}x - \dfrac{1}{3}\left( {\dfrac{4}{9}x} \right) = \dfrac{8}{{27}}x$ liter of Dettol is remaining in the bottle
$\dfrac{5}{9}x - \dfrac{1}{3}\left( {\dfrac{5}{9}x} \right) + \dfrac{1}{3}x = \dfrac{{19}}{{27}}x$ liter of water is present.
Fourth operation:
Again $\dfrac{1}{3}$ part of mixture is taken out, so we have now remaining in the bottle is
$\dfrac{8}{{27}}x - \dfrac{1}{3}\left( {\dfrac{8}{{27}}x} \right) = \dfrac{{16}}{{81}}x$ liter of Dettol will be finally remaining in the bottle
$\dfrac{{19}}{{27}}x - \dfrac{1}{3}\left( {\dfrac{{19}}{{27}}x} \right) + \dfrac{1}{3}x = \dfrac{{65}}{{81}}x$ liter of water will be finally remaining in the bottle.
Now we have to find ratio of Dettol and water
$ = \dfrac{{\dfrac{{16}}{{81}}x}}{{\dfrac{{65}}{{81}}x}} = \dfrac{{16}}{{65}} = 16:65$
Hence option C is the correct option.

Note: Whenever you get this type of question the key concept of solving is you have to just find ratio after simple mathematical calculation. All you have to do is focus on your calculation and care about the amount remaining in the previous operation so that mistakes can not happen.