Unit Price and Cost-Per-Unit Comparisons
"Which pack is the better deal?" looks like a shopping question, but it is really a ratio-and-proportion problem, and versions of it appear regularly in Class 6–8 "Comparing Quantities" chapters, in quantitative-aptitude sections of entrance exams, and in word problems that test whether you compare like with like. The rule is simple, but skipping the unit-conversion step is where most marks are lost.
The unit price formula
The quantity must be in the same unit for every option you are comparing — grams, not a mix of grams and kilograms; millilitres, not a mix of millilitres and litres. This single check is what most "trick" comparison questions are testing.
Worked example 1 — same units, direct comparison
Pack A: 500 g for ₹150. Pack B: 750 g for ₹210. Which is cheaper per gram?
Unit price of A = 150 ÷ 500 = ₹0.30 per gram
Unit price of B = 210 ÷ 750 = ₹0.28 per gram
Pack B is cheaper per gram.
Worked example 2 — different units, must convert first
Pack C: 1 kg for ₹280. Pack D: 400 g for ₹115. Compare the unit price per gram.
Convert Pack C to grams first: 1 kg = 1000 g.
Unit price of C = 280 ÷ 1000 = ₹0.28 per gram
Unit price of D = 115 ÷ 400 = ₹0.2875 per gram
Pack C is cheaper per gram, even though its total price looks higher at
first glance — comparing the sticker prices (₹280 vs ₹115) directly, without converting
units, would have suggested the opposite.
Worked example 3 — expressing the saving as a percentage
Using the unit prices from Example 1 (A = ₹0.30/g, B = ₹0.28/g), what percentage does buying B save compared to A?
Saving per gram = 0.30 − 0.28 = ₹0.02
Percentage saving = (0.02 ÷ 0.30) × 100 = 6.67%
Always divide the saving by the more expensive option's price to get the correct percentage saving — dividing by the cheaper price instead is a common error that overstates the saving.
Worked example 4 — a multi-buy offer
A shop offers "buy 2, get 1 free" on 200 mL bottles priced at ₹45 each — so 3 bottles (600 mL total) cost ₹90 (only 2 are paid for). A rival single large bottle holds 500 mL for ₹80. Which is the better unit price?
Multi-buy: unit price = 90 ÷ 600 = ₹0.15 per mL
Single bottle: unit price = 80 ÷ 500 = ₹0.16 per mL
The multi-buy offer is cheaper per millilitre, even though its total spend
(₹90) is higher than the single bottle (₹80) — total price alone never tells you which
option is the better value.
Common mistakes that cost marks
- Comparing total (sticker) prices instead of unit prices — a bigger pack costing more is not automatically the worse deal, and a smaller pack costing less is not automatically the better one.
- Forgetting to convert units before comparing — comparing ₹/kg against ₹/g directly, without converting one of them first, gives a meaningless ratio.
- Dividing the saving by the wrong price when computing a percentage saving (see Example 3).
- Ignoring "get X free" offers and comparing only the price of the items actually paid for, rather than the total quantity received.
Where this is tested
| Level | Typical use |
|---|---|
| CBSE Class 6–8 (Comparing Quantities, Ratio and Proportion) | Direct unit-price and best-buy word problems |
| Class 10 and CUET quantitative reasoning | Multi-step comparison problems with unit conversion |
| General competitive-exam aptitude sections | Fast unit-price comparisons under time pressure |
Do the division instantly. Use the calculator suite to check unit-price arithmetic and percentage savings without long division on paper.
Open the ABC Chemistry Calculator Suite →This kind of ratio-and-proportion reasoning underpins a lot of school-level maths. ABC Chemistry's Class 11–12 coaching, at its Gurugram centre and online across India, builds these foundations alongside board-exam chemistry — details at abcchemistry.in.