How to Solve False Weight Profit Problems
Solve false weight and dishonest dealer profit aptitude problems with the true-weight ratio formula, a worked example, and practice MCQs.
Expected Interview Answer
A dealer using a false weight but claiming a genuine or fixed profit percentage earns an actual profit of Profit% = (True Weight - False Weight) / False Weight x 100, since the dealer effectively sells less quantity while charging for the full labeled amount.
If a dealer claims to sell at cost price but uses a weight of only 900 grams for every claimed 1000 grams, they are really giving the customer 900 grams while charging the price of 1000 grams, so the profit percentage equals (1000-900)/900 x 100. This is structurally identical to a goods-quantity version of profit and loss: the 'cost' is what the dealer actually gives (true weight), and the 'revenue' is what they charge for (claimed weight). When a dealer both marks up the price AND uses a false weight, the two effects combine multiplicatively using the successive-percentage-change shortcut: Net Profit% = markup% + weight-error% + (markup% x weight-error%)/100. Always identify whether the discrepancy is in the numerator (extra revenue) or denominator (short weight) before applying the ratio.
- Reduces false-weight problems to a familiar profit-percentage ratio
- Combines markup and short-weighting using the successive-change formula
- Prevents confusing which quantity is the true “cost” basis
AI Mentor Explanation
A groundskeeper claims to lay 100 meters of pitch-covering material per over’s worth of payment but actually only lays 90 meters, pocketing the material cost of the missing 10 meters while billing for the full 100. The effective overcharge is (100-90)/90 x 100 = 11.11%, computed on what was ACTUALLY delivered (the true amount), not on the claimed amount. False-weight problems always anchor the profit percentage on the true, short-delivered quantity as the base.
Worked example
Claimed weight
- 1000 grams
True (false) weight used
- 900 grams
Profit%
- (1000-900)/900 x 100
- = 11.11%
Step-by-Step Explanation
Step 1
Identify true vs claimed quantity
True weight is what is actually given; claimed weight is what is charged for.
Step 2
Apply the ratio
Profit% = (Claimed - True) / True x 100, mirroring standard profit percentage on cost.
Step 3
Combine with any stated markup
If a markup% is also charged, use Net% = markup% + weight-error% + (markup% x weight-error%)/100.
Step 4
Sanity-check the base
Always divide by the TRUE (short) quantity, never the claimed quantity, since that is the effective “cost” basis.
What Interviewer Expects
- Correctly identifying true weight as the base (denominator) of the ratio
- Recognizing the structural equivalence to standard profit-percentage-on-cost problems
- Correctly combining a stated markup with a weight discrepancy using the successive-change formula
- Avoiding the common error of dividing by the claimed weight instead of the true weight
Common Mistakes
- Dividing by the claimed (labeled) weight instead of the true (actual) weight
- Treating the weight shortfall and any price markup as simply additive instead of multiplicative
- Confusing which quantity represents the dealer's true cost basis
- Forgetting that “selling at cost price” with a false weight still yields a genuine profit
Best Answer (HR Friendly)
“A false-weight dealer who claims to sell at cost is still making a profit, because they are giving less than what they charge for. I calculate it the same way as a standard profit-percentage problem — the true quantity actually given is the cost basis, and the difference between what is claimed and what is truly given, divided by the true quantity, gives the profit percentage. If there is also a stated markup, I combine the two effects using the successive-percentage-change shortcut rather than just adding them.”
Follow-up Questions
- How would the profit percentage change if the dealer also marks up the price by 10% in addition to using a false weight?
- How is this problem structurally similar to standard profit-and-loss on cost price?
- What single false weight would a dealer need to use to achieve exactly 25% profit while claiming cost price?
- How would you extend this to a dealer using two different false weights when buying and selling?
MCQ Practice
1. A dealer claims to sell rice at cost price but uses a weight of 800g for every claimed 1000g. The dealer's profit percentage is?
Profit% = (1000-800)/800 x 100 = 200/800 x 100 = 25%.
2. A shopkeeper sells goods at cost price using a weight of 950g instead of 1000g. His profit percentage is closest to?
Profit% = (1000-950)/950 x 100 = 50/950 x 100 ≈ 5.26%.
3. A dealer marks up price by 10% and also uses a false weight giving only 900g per claimed 1000g. The overall profit percentage is?
Weight-error% = (1000-900)/900 x 100 = 11.11%. Net% = 10 + 11.11 + (10 x 11.11)/100 = 10 + 11.11 + 1.11 = 22.22%.
Flash Cards
False-weight profit formula? — Profit% = (Claimed weight - True weight) / True weight x 100.
What is the correct base (denominator)? — The TRUE (actually given) weight, since it is the effective cost basis.
How to combine markup with false weight? — Net% = markup% + weight-error% + (markup% x weight-error%)/100.
Can “selling at cost price” still yield profit? — Yes — if a false (short) weight is used, a genuine profit is earned despite the cost-price claim.