Question

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. The quantity of alcohol in the given mixture is:

• A. 4 litres
• B. 5 litres
• C. 10 litres
• D. 9 litres

Hint:

- In ratio problems, set up an equation based on the initial and final ratios, and solve for the unknown variable.

Answer 1

The Correct Option is C

Step 1: Defining the Variables
Let the initial quantity of alcohol in the mixture be \( 4x \) litres and the initial quantity of water in the mixture be \( 3x \) litres, based on the given ratio of 4:3. Step 2: Adding Water to the Mixture
When 5 litres of water is added to the mixture, the quantity of water becomes \( 3x + 5 \). The new ratio of alcohol to water becomes 4:5, so we can write the equation: \[ \frac{4x}{3x + 5} = \frac{4}{5} \] Step 3: Solving the Equation
Cross-multiply to solve for \( x \):
\[ \begin{aligned} 4x \times 5 &= 4 \times (3x + 5)
20x &= 12x + 20
20x - 12x &= 20
8x &= 20
x &= 2.5 \end{aligned} \] Step 4: Finding the Quantity of Alcohol
The quantity of alcohol in the mixture is \( 4x = 4 \times 2.5 = 10 \) litres. Thus, the quantity of alcohol in the given mixture is 10 litres. Therefore, the correct answer is (3) 10 litres.