What was the quantity of alcohol in the mixture initially?

A mixture contains alcohol and water in the ratio of 5:4. If 18 L of water is added to the mixture, the ratio of alcohol and water becomes 4:5. What was the quantity of alcohol in the mixture initially

  1. 36 L
  2. 32 L
  3. 40 L
  4. None of these
Anurag Mishra Professor Asked on 19th December 2015 in Maths.
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1 Answer(s)

Answer: (3) 40 L

Solution:-
The ratio of alcohol and water in a mixture = 5: 4

Then, let the quantity of alcohol and water in the same mixture be 5 X & 4 X

If 18 L of water is added to the mixture , the ratio of alcohol and water becomes 4: 5.
Then    5 X / (4 X + 18) = 4/5
By cross multiplication,
5 x 5 X =  4 x 4 X + 18 x 4
25 X = 16 X + 72
25 X – 16 X = 72
9 X = 72
X = 72/9
X = 8

Then the quantity of alcohol 5 X = 5 x 8 = 40 L and quantity of water 8 x 4 = 32 L

Hence, the correct answer is option (3) 40 L.

Anurag Mishra Professor Answered on 20th December 2015.
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