A mixture contains alcohol and water in the ratio 4 : 3. If 5 litres of water…
2024
A mixture contains alcohol and water in the ratio 4 : 3. If 5 litres of water is added to the mixture, the ratio becomes 4: 5. Find the quantity of alcohol in the given mixture.
- A.
10 litres
- B.
7.5 litres
- C.
5 litres
- D.
12.5 litres
Attempted by 27 students.
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Correct answer: A
Solution:
Let the quantity of alcohol be 4x litres and water be 3x litres.
After adding 5 litres of water the new ratio becomes 4:5, so set up the equation:
4x / (3x + 5) = 4/5
Cross-multiply: 20x = 4(3x + 5)
Expand: 20x = 12x + 20
Solve: 20x − 12x = 20 ⇒ 8x = 20 ⇒ x = 20/8 = 2.5
Therefore, alcohol = 4x = 4 × 2.5 = 10 litres.