Question 2

To check if volume and price are proportional, we need to calculate the price per unit volume for each container.

Step 1 — Understand Proportionality

Two quantities are proportional if their ratio is always constant. In this case, if price is proportional to volume, then the price divided by the volume should be the same for all containers. We will calculate the price per milliliter (₹/mL) for each container.

Step 2 — Calculate Price per mL for Sachet

Let us find the price per milliliter for the sachet.

$\text{Price per mL (Sachet)} = \frac{\text{Price}}{\text{Volume}}$

$= \frac{₹2}{6 \text{ mL}}$

$= 0.3333... \text{ ₹/mL}$

$\boxed{0.33 \text{ ₹/mL}}$

Step 3 — Calculate Price per mL for Small Bottle

Next, we find the price per milliliter for the small bottle.

$\text{Price per mL (Small Bottle)} = \frac{\text{Price}}{\text{Volume}}$

$= \frac{₹154}{180 \text{ mL}}$

$= 0.8555... \text{ ₹/mL}$

$\boxed{0.86 \text{ ₹/mL}}$

Step 4 — Calculate Price per mL for Medium Bottle

Now, let us calculate the price per milliliter for the medium bottle.

$\text{Price per mL (Medium Bottle)} = \frac{\text{Price}}{\text{Volume}}$

$= \frac{₹276}{340 \text{ mL}}$

$= 0.8117... \text{ ₹/mL}$

$\boxed{0.81 \text{ ₹/mL}}$

Step 5 — Calculate Price per mL for Large Bottle

Finally, we determine the price per milliliter for the large bottle.

$\text{Price per mL (Large Bottle)} = \frac{\text{Price}}{\text{Volume}}$

$= \frac{₹540}{1000 \text{ mL}}$

$= 0.54 \text{ ₹/mL}$

$\boxed{0.54 \text{ ₹/mL}}$

Step 6 — Compare Price per mL Values

We have calculated the price per mL for each container size.

The price per mL for the Sachet is 0.33 ₹/mL. The price per mL for the Small Bottle is 0.86 ₹/mL. The price per mL for the Medium Bottle is 0.81 ₹/mL. The price per mL for the Large Bottle is 0.54 ₹/mL.

These values are not the same. If volume and price were proportional, all these values would be equal.

Answer

The price per mL for the Sachet is 0.33 ₹/mL. The price per mL for the Small Bottle is 0.86 ₹/mL. The price per mL for the Medium Bottle is 0.81 ₹/mL. The price per mL for the Large Bottle is 0.54 ₹/mL. Since the price per mL is not the same for all containers, the volume of shampoo is not proportional to the price.