Question 14
Context: The volume of a sachet is 6 mL and its price is ₹2. The volume of a small bottle is 180 mL and its price is ₹154. The ratio of the volume of a sachet to a small bottle is 6 : 180. The ratio of their prices is 2 : 154.
Q. Why do you think that the ratio of the prices is not proportional to the ratio of the volumes?
When two quantities are directly proportional, the ratio of their corresponding values is constant.
Step 1 — Calculate the unit price for the sachet
Let us find the price per milliliter (mL) for the sachet.
The volume of the sachet is 6 mL. The price of the sachet is ₹2.
Step 2 — Calculate the unit price for the small bottle
Let us find the price per milliliter (mL) for the small bottle.
The volume of the small bottle is 180 mL. The price of the small bottle is ₹154.
Step 3 — Compare the unit prices
We compare the unit prices we calculated for the sachet and the small bottle.
The unit price for the sachet is approximately ₹0.333 per mL. The unit price for the small bottle is approximately ₹0.856 per mL.
Since these unit prices are not equal, the ratio of the prices is not proportional to the ratio of the volumes. If they were proportional, the price per mL would be the same for both.
Answer
The ratio of the prices is not proportional to the ratio of the volumes because the price per unit volume (per mL) is different for the sachet and the small bottle. If the ratios were proportional, the unit price would be the same for both.
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