# Mixture and Allegation Problems

A 10 litre container holds a mixture of water and sugar, the volume of sugar being 15% of total volume. A few litres of the mixture is released and an equal amount of water is added. Then the same amount of the mixture as before is released and replaced with water for a second time. As a result, the sugar content becomes 10% of the total volume. What is the approximate quantity of mixture released each time?

I have tried:

Let the total litres be 10.

In that, let 15 percent be sugar so sugar contains 1.5 litres of the total volume of the mixture.

Then I calculated the ratio to be 1.5:8.5. For ratio calculating, I have taken the value as whole numbers, that is, 15:85.

Ratio is 3:17.

Let some amount of mixture released be x

3x/20 *1.5 + 17x/20*8.5

Then an equal amount of water is added in the mixture

so

3x/20*1.5 + 17x/20*8.5 + x

Second time same process is repeated means 10% of the total volume

(3x/20)^2*1.5 + (17x/20)*8.5 +2x

For that

(3x/20)^2*1.5/(17x/20)*8.5 +2x = 1/9

I am doing this question correctly? If not, where is my mistake?

Please, anyone, guide me to the answer.

options are

1.)1 litre 2.) 1.5 litre 3.) 1.2 litres 4.) 2 litres

• What is your answer and what is the answer in book? – Kanwaljit Singh Mar 19 '17 at 17:34
• options are 1.)1 litre 2.) 1.5 litre 3.) 1.2 litres 4.) 2 litres these are the options given @KanwaljitSingh – Learning user Mar 20 '17 at 5:12
• @SchrodingersCat please guide me for this Question – Learning user Mar 20 '17 at 7:32
• @KanwaljitSingh I did not get any answer?How to solve this – Learning user Mar 20 '17 at 8:53