# 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

- 36 L
- 32 L
- 40 L
- None of these

**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.