False Weight: Formula, Tricks and Solved Questions

False Weight questions deal with incorrect measures used during buying or selling. A trader may give less quantity while charging for the stated quantity, or receive more quantity while paying for the stated quantity. The solution depends on comparing the actual quantity with the quantity shown by the false weight.

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What Is False Weight?

False weight means using a measure whose actual quantity differs from its marked or stated quantity. The profit or loss is calculated by comparing the actual quantity exchanged with the quantity for which payment is made.

If a seller gives only W units while charging for W + d units, the extra quantity charged creates a gain. The gain percentage is calculated on the actual quantity given: gain% = (d/W) × 100. For example, if 900 g is given as 1 kg, the gain is based on 900 g, not 1 kg.

False Weight Formula & Tricks

Important Formulas

Gain when less quantity is given
Gain% = [(Stated quantity − Actual quantity) / Actual quantity] × 100

Use this when the seller charges for the stated quantity but gives a smaller actual quantity.

Loss when more quantity is given
Loss% = [(Actual quantity − Stated quantity) / Actual quantity] × 100

Use this when the seller charges for the stated quantity but gives a larger actual quantity.

Gain when more quantity is received while buying
Gain% = [(Actual quantity received − Paid quantity) / Paid quantity] × 100

Use this when a trader pays for a smaller stated quantity but receives more goods.

Required false weight for a given gain
False weight = Standard weight × 100 / (100 + Gain%)

This gives the actual quantity to be given when the seller wants a specified gain by charging for the standard quantity.

Quick Tricks

Use the actual quantity as the denominator for selling

When a seller gives less quantity but charges for the full quantity, calculate gain on the quantity actually delivered.

Example: For 800 g sold as 1 kg, gain% = (1000 − 800)/800 × 100 = 25%.
Use the paid quantity as the denominator while buying

When a trader receives more quantity than the quantity paid for, calculate gain on the quantity recorded or paid for.

Example: If 1 kg is paid for but 1.25 kg is received, gain% = (1.25 − 1)/1 × 100 = 25%.
Convert units before calculation

Use the same unit for both quantities. Convert kilograms to grams or grams to kilograms before applying the formula.

Example: For 1 kg and 900 g, write them as 1000 g and 900 g before calculating.

False Weight Concepts

Less Quantity Given at the Stated Price

A seller gains when the actual quantity given is less than the quantity written or promised, while the buyer pays for the larger stated quantity.

If the standard quantity is S and the actual quantity is A, then gain% = [(S − A)/A] × 100. The denominator is A because the seller's cost is related to the quantity actually supplied. For 1 kg charged but 800 g supplied, gain% = 200/800 × 100 = 25%.

Example: A shopkeeper sells 900 g as 1 kg. Gain% = (1000 − 900)/900 × 100 = 100/9% = 11 1/9%.

More Quantity Received While Buying

A trader gains while buying when the actual quantity received is greater than the quantity for which payment is made.

If the paid quantity is P and the actual quantity received is A, then gain% = [(A − P)/P] × 100. Here, the trader receives additional goods without additional payment. If 1 kg is paid for and 1.2 kg is received, gain% = 0.2/1 × 100 = 20%.

Example: A trader pays for 800 g but receives 1 kg. Gain% = (1000 − 800)/800 × 100 = 25%.

Finding the Actual Quantity for a Desired Gain

To earn a gain of r% while charging for a standard quantity S, the actual quantity supplied must be S × 100/(100 + r).

The selling value of the stated quantity is treated as 100 + r parts, while the cost of the actual quantity is treated as 100 parts. Thus, actual quantity = S × 100/(100 + r). For a 25% gain on 1 kg, actual quantity = 1000 × 100/125 = 800 g.

Example: For a 20% gain on 1 kg, the seller should give 1000 × 100/120 = 833 1/3 g.

Finding the Gain from a Given False Weight

When a seller gives A units but charges for S units, the gain percentage is (S − A)/A × 100, provided the price per unit remains unchanged.

The excess quantity charged is S − A. Since the seller's cost is based on A units actually given, divide the excess by A. If the false measure is heavier than the standard and the seller gives more than charged, the same comparison produces a loss instead.

Example: If 1.1 kg is given while charging for 1 kg, loss% = (1.1 − 1)/1.1 × 100 = 100/11% = 9 1/11%.

False Weight Video Lessons

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6 Lessons
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Dishonest Shopkeeper False Weight Problems

Understand how to solve profit and loss problems involving dishonest shopkeepers who use false weights, including calculating effective gain through quantity-based analysis.

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Practice False Weight Questions

Practise published questions related to this topic.

1A shopkeeper buys an electronic item for ₹ 2,400. He marks it at a certain price so that after allowing a 20% discount, he still makes a 20% profit on his cost price. Find the marked price of the item.→ 2After allowing a discount of 50% on the marked price of an article, it is sold for ₹61,649. Find its marked price (in ₹).→ 3A smartwatch originally priced at ₹6,000 is now being sold at a 25% discount. What is the sale price?→ 4A shopkeeper offers the following schemes on toys of the same marked price. (A) Successive discounts of 24% and 33% on any number of toys bought. (B) Successive discounts of 39%, 37% and 23% on any number of toys bought. (C) 24% discount on the first 2 toys and 12% discount on each toy thereon. (D) 2 toys free of cost on buying 5 toys. A customer wants to buy 5 toys. Which of the above schemes is the least beneficial to her?→ 5A shopkeeper offers the following four schemes. A) Two successive discounts of 28% and 28% B) Buy 1, get 4 C) Discount of 35% D) Two successive discounts of 27% and 26% Which scheme is best for the customer?→ 6A person sells 50 chairs for ₹10,000, suffering a loss of 15%. Estimate how many chairs should he sell for ₹9000 to make a profit of 10%?→ 7If an item marked at ₹3,392 is sold for ₹1,696, then what is the discount percentage?→ 8Find the rate of discount when the marked price is ₹11,280 and the selling price is ₹9,588.→ 9A cash payment that will settle a bill for 625 pairs of boots at ₹94 per pair of boots with successive discounts of 20% and 7% with a further discount of 20% on cash payment is:→ 10Find the single discount equivalent to two successive discounts of 29% and 28%.→

False Weight Quick Quiz

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Quick Revision Notes

False Weight Quick Revision

Use the quantity comparison and choose the correct denominator before calculating the percentage.

  • Less quantity given while charging for more: gain% = (stated − actual)/actual × 100.
  • More quantity given while charging for less: loss% = (actual − stated)/actual × 100.
  • More quantity received while paying for less: gain% = (actual received − paid quantity)/paid quantity × 100.
  • For a desired gain of r%, actual quantity supplied = standard quantity × 100/(100 + r).
  • Convert all quantities to the same unit before applying a formula.
  • In selling questions, the denominator is generally the actual quantity supplied because it represents the cost quantity.

False Weight FAQs

What is the false weight formula when 900 g is sold as 1 kg?

Gain% = (1000 − 900)/900 × 100 = 100/9% = 11 1/9%.

A seller gives 800 g instead of 1 kg. What is the gain percentage?

Gain% = (1000 − 800)/800 × 100 = 25%.

How much should be given for a 20% gain on 1 kg?

Actual quantity = 1000 × 100/120 = 833 1/3 g.

A trader pays for 1 kg but receives 1.25 kg. What is the gain?

Gain% = (1.25 − 1)/1 × 100 = 25%.

If a seller gives 1.1 kg while charging for 1 kg, is it gain or loss?

It is a loss because more quantity is supplied than charged. Loss% = (1.1 − 1)/1.1 × 100 = 100/11% = 9 1/11%.

Why is actual quantity used as the denominator when a seller gives less weight?

The seller's cost is based on the quantity actually supplied. Therefore, gain percentage is calculated as excess quantity divided by actual quantity supplied.

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