Question

A bottle is full of dettol One third of it is taken out and then an equal amount of water is poured into the bottle to fill it This operation is done four times Find the final ratio of dettol and water in the bottle

• A. 13 : 55
• B. 20 : 74
• C. 16 : 65
• D. 10 : 48

Answer 1

Answer: (C)

16 : 65

Let the original quantity of dettol in the bottle be x litres
Then quantity of water in the bottle = 0 litres After the 1st operation : Quantity of dettol in the bottle
$=(x-\frac{x}{3})litres=\frac{2x}{3}litres$
Quantity of water in the bottle $=\frac{2x}{3}litres$
After the 2nd operation : Quantity of dettol in the bottle $=(\frac{2x}{3}-\frac{1}{3}\times \frac{2x}{3})litres=\frac{4x}{9}litres$
$\therefore$ Quantity of water in the bottle = $(\frac{x}{3}+\frac{2x}{9})litres$
After the third operation : Quantity of dettol in the bottle $=(\frac{4x}{9}-\frac{1}{3}\times \frac{4x}{9})litres=\frac{8x}{7}litres$
$\therefore$ Quantity of water in the bottle $=(\frac{x}{3}+\frac{2x}{9}+\frac{4x}{27})litres$
After the fourth operation : Quantity of dettol in the bottle $=(\frac{8x}{27}-\frac{1}{3}\times \frac{8x}{27})litres=\frac{16x}{81}litres$
Quantity of water in the bottle $=(\frac{x}{3}+\frac{2x}{9}+\frac{4x}{27}+\frac{8x}{81})litres=\left(\frac{27x+18x+12x+8x}{81}\right)litres=\frac{65x}{81}litres$
$\therefore$ Required ratio $=\frac{16x}{81}:\frac{65x}{81}=16:65$