NIMCET 2026 — Reasoning PYQ

To solve this problem from image_808ba2.png, we can use algebra to find the volume drawn from each container.

1. Define Variables:

Let $x$ be the volume drawn from container A and $y$ be the volume drawn from container B.

We know the total volume required is 2.1 litres:

$$x+y=2.1$$

$$y=2.1-x$$

2. Analyze the Ratios:

• Container A (ratio 5:3):

  • Alcohol fraction = $\frac{5}{8}$

  • Water fraction = $\frac{3}{8}$

• Container B (ratio 1:3):

  • Alcohol fraction = $\frac{1}{4}$ (or $\frac{2}{8}$)

  • Water fraction = $\frac{3}{4}$ (or $\frac{6}{8}$)

3. Set up the Equation:

The final mixture must have equal quantities of alcohol and water. Since the total is 2.1 litres, each component must be $1.05$ litres ($\frac{2.1}{2}=1.05$).

Using the alcohol component equation:

$$\frac{5}{8}x+\frac{1}{4}y=1.05$$

4. Solve for $x$:

Substitute $y=2.1-x$ into the equation:

$$\frac{5}{8}x+\frac{2}{8}(2.1-x)=1.05$$

Multiply the entire equation by 8 to clear the denominator:

$$5x+2(2.1-x)=1.05\times 8$$

$$5x+4.2-2x=8.4$$

$$3x=8.4-4.2$$

$$3x=4.2$$

$$x=\frac{4.2}{3}$$

$$x=1.4$$

The amount of liquid to be drawn from container A is 1.4 litres.

Correct Answer: Option 1