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The ladder / Level 1 · Trader/ Business math

Unit conversions and per-unit prices

Quintals, tonnes, cases and gross; comparing packs by price per kg or litre; and pricing after loss in handling.

How numbers are rounded on these pages. Calculations are done at full precision and rounded only at the end, half up. Rupee amounts are rounded to the nearest rupee unless shown with paise, in which case to the nearest paisa. Percentages are shown to two decimal places, and days to one decimal place. Break-even quantities and reorder levels are rounded up to the next whole unit, because rounding down would leave you short. Economic order quantity is rounded to the nearest whole unit. Interest for a number of days uses a 365-day year. All examples and quiz questions are Hypothetical: they show the method, not real prices or rates.

Unit conversions and per-unit prices

Suppliers quote by the quintal, tonne, case or gross; customers buy by the kilo, litre, pack or piece. Many pricing mistakes are really conversion mistakes. The fix is simple: convert everything to the same unit before comparing or pricing, and work out the price per unit (per kg, per litre, per piece).

If some of what you buy is lost in cleaning, sorting, breakage or drying, spread the full cost over only the usable quantity.

The standard formulas

Common Indian trade units1 kg = 1,000 g1 quintal = 100 kg1 tonne = 1,000 kg = 10 quintals1 litre = 1,000 ml1 dozen = 121 gross = 144 (12 dozen)
Per-unit pricePrice per unit = Total priceQuantity in that unit
Allowing for lossCost per usable unit = Total cost (including freight)Quantity bought × (1 − loss %)

Terms used

Quintal
100 kg. Common for grain, pulses and other farm produce.
Tonne (metric ton)
1,000 kg.
Gross
144 pieces, or 12 dozen.
Per-unit (unit) price
The price for one standard unit, such as per kg or per litre, so packs of different sizes can be compared.

Worked examples

HypotheticalBasicWhich pack is cheaper?

A 500 g pack costs ₹56 and a 1 kg pack costs ₹105.

  • 500 g pack: ₹56 ÷ 0.5 kg = ₹112 per kg
  • 1 kg pack: ₹105 per kg

The 1 kg pack is cheaper by ₹7 per kg.

HypotheticalIntermediateFrom case price to per-pack and per-kg

A case of 24 packs of 200 g costs ₹1,080. A shop sells each pack at ₹50.

  • Cost per pack = ₹1,080 ÷ 24 = ₹45
  • Weight per case = 24 × 200 g = 4.8 kg; cost per kg = ₹1,080 ÷ 4.8 = ₹225
  • Margin per pack = (₹50 − ₹45) ÷ ₹50 = 10.00%

HypotheticalAdvancedQuintal rate to a per-kg selling price, with loss

A trader buys rice at ₹4,200 per quintal plus ₹150 freight per quintal. About 2% is lost in cleaning and handling. He wants a 10% margin.

  • Cost per quintal delivered = ₹4,350; usable rice = 100 kg × 98% = 98 kg
  • Cost per usable kg = ₹4,350 ÷ 98 = ₹44.39
  • Price for a 10% margin = ₹44.39 ÷ 0.90 = ₹49.32 per kg

Pricing from ₹42 per kg alone, without freight and loss, would have given ₹46.67.

Quiz: unit conversions and per-unit prices

Pick an answer to see at once whether it is right, with a short explanation. Each question takes one try; your score appears at the end. No answers are sent anywhere. (Without JavaScript, open “Show answer” under each question.)

  1. Units and unit prices · BasicHow many quintals are there in 2.5 tonnes?
    Show answer

    Answer: (c) 25

    1 tonne = 10 quintals, so 2.5 tonnes = 25 quintals (2,500 kg).

    Why the other options are wrong:

    • (a) That would be 25 tonnes.
    • (b) That is still in tonnes.
    • (d) That is kilograms, not quintals.
  2. Units and unit prices · BasicA 750 ml bottle costs ₹90. What is the price per litre?
    Show answer

    Answer: (b) ₹120.00

    ₹90 ÷ 0.75 litre = ₹120 per litre.

    Why the other options are wrong:

    • (a) That multiplies by 0.75 instead of dividing.
    • (c) A decimal slip: 750 ml is 0.75 litre.
    • (d) That is the price per ml, not per litre.
  3. Units and unit prices · IntermediateA 400 g pack costs ₹48 and a 1.5 kg pack costs ₹172.50. Which is cheaper per kg?
    Show answer

    Answer: (b) The 1.5 kg pack: ₹115 per kg against ₹120

    ₹48 ÷ 0.4 = ₹120 per kg; ₹172.50 ÷ 1.5 = ₹115 per kg.

    Why the other options are wrong:

    • (a) Compare per kg, not the pack price.
    • (c) ₹120 and ₹115 are not the same.
    • (d) ₹172.50 ÷ 1.5 is ₹115, not ₹125.
  4. Units and unit prices · IntermediateA carton of 12 bottles of 500 ml costs ₹1,440. What is the cost per litre?
    Show answer

    Answer: (b) ₹240

    12 × 0.5 litre = 6 litres. ₹1,440 ÷ 6 = ₹240 per litre.

    Why the other options are wrong:

    • (a) That is the cost per bottle (half a litre).
    • (c) That doubles the per-litre cost.
    • (d) A slip in units: 12 × 500 ml is 6 litres, not 600.
  5. Units and unit prices · IntermediateOne gross of pens costs ₹1,296. What is the cost per pen?
    Show answer

    Answer: (c) ₹9

    ₹1,296 ÷ 144 = ₹9 per pen.

    Why the other options are wrong:

    • (a) That is the cost per dozen.
    • (b) A gross is 144, not 100.
    • (d) A gross is 144, not 120.
  6. Units and unit prices · AdvancedYou buy 50 kg at ₹60/kg. About 4% is lost in sorting. What is the cost per usable kg?
    Show answer

    Answer: (d) ₹62.50

    ₹3,000 ÷ 48 usable kg = ₹62.50.

    Why the other options are wrong:

    • (a) That adds 4% to the price, which slightly understates the cost.
    • (b) Loss makes each usable kg cost more, not less.
    • (c) That ignores the loss.
  7. Units and unit prices · AdvancedGrain costs ₹3,600 per quintal plus ₹100 freight per quintal, and 1.5% is lost in handling. What price per kg gives an 8% margin?
    Show answer

    Answer: (a) ₹40.83

    Cost per usable kg = ₹3,700 ÷ 98.5 = ₹37.56. Price = ₹37.56 ÷ 0.92 = ₹40.83.

    Why the other options are wrong:

    • (b) That ignores the 1.5% loss.
    • (c) That is an 8% markup, not margin.
    • (d) That ignores freight and loss.