How to Solve Dishonest Dealer Problems
Solve dishonest dealer aptitude problems combining buying and selling false weights, with the shortcut formula and practice questions.
Expected Interview Answer
A dishonest dealer’s overall gain percentage combines every trick used — false weights when buying, false weights when selling, and any stated markup — by chaining each individual effect as a multiplying factor using the successive-percentage-change formula, not by adding the individual gains.
A dealer may cheat while buying (getting more than they pay for, e.g. claiming to buy 1000g but actually taking 1050g), while selling (giving less than charged, e.g. claiming to give 1000g but actually giving 900g), or both at once. Each individual trick converts to a gain percentage using the standard ratio: (difference/true or claimed base) x 100, exactly like a single false-weight problem. When multiple tricks combine, the dealer’s total factor is the product of each individual factor, so the overall gain is computed via a + b + ab/100, generalized to three terms if a price markup is also present. The single most powerful shortcut for the classic 'buys and sells with the same false weight, claiming cost price' scenario is Gain% = (Error in weight / (True weight - Error)) x 100, which is derived by combining the buying-side and selling-side false weights into one net weight ratio before applying the ratio.
- Reduces multi-trick dealer scams to a single combined-factor calculation
- Reuses the false-weight ratio and successive-percentage-change shortcut together
- Provides a direct shortcut formula for the classic buy-and-sell same-false-weight case
AI Mentor Explanation
A kit supplier claims to buy back used cricket gear at a fair per-kilogram rate but rigs the scale so a claimed 1000g bag actually weighs 1050g when the supplier receives it, meaning they got extra gear for the stated price — a buying-side gain of (1050-1000)/1000 x 100 = 5%. If the same supplier also shortchanges when reselling new gear, giving only 900g of stated 1000g bags, that is a separate selling-side gain of (1000-900)/900 x 100 = 11.11%. Combining both, using a + b + ab/100 = 5 + 11.11 + (5)(11.11)/100 ≈ 16.67%, is exactly how dishonest-dealer problems chain multiple false-weight tricks into one net figure.
Worked example (buys and sells with false weights)
Buying-side gain
- (1050-1000)/1000 x 100 = 5%
Selling-side gain
- (1000-900)/900 x 100 = 11.11%
Combined gain
- 5+11.11+0.556 ≈ 16.67%
Step-by-Step Explanation
Step 1
Isolate each individual trick
Compute a separate gain percentage for buying-side false weight, selling-side false weight, and any stated markup.
Step 2
Use the correct base for each ratio
Buying-side gain uses the claimed (paid-for) amount as base; selling-side gain uses the true (delivered) amount as base.
Step 3
Chain all individual gains
Combine two gains a and b via a + b + ab/100; extend to three terms if a markup is also present.
Step 4
Apply the same-weight shortcut when relevant
For “buys and sells with the same false weight, claims cost price,” use Gain% = Error/(True - Error) x 100 directly.
What Interviewer Expects
- Correctly separating buying-side gain from selling-side gain before combining
- Using the right base (claimed vs true quantity) for each individual ratio
- Chaining multiple gains multiplicatively via the successive-change formula, not adding them
- Recognizing and applying the same-false-weight shortcut for the classic buy-and-sell scenario
Common Mistakes
- Simply adding the buying-side and selling-side gain percentages instead of chaining them
- Using the wrong base (claimed vs true weight) for one of the two individual ratios
- Forgetting to include a stated price markup as a third chained factor when present
- Misapplying the same-weight shortcut formula when the buying and selling weights actually differ
Best Answer (HR Friendly)
“I break a dishonest dealer’s scam into each individual trick — cheating on the buy side, cheating on the sell side, and any price markup — and compute a separate gain percentage for each using the right base for that ratio. Then I chain all of them together using the successive-percentage-change formula, a plus b plus ab over 100, rather than just adding the percentages, because each trick compounds on top of the others rather than stacking flatly.”
Follow-up Questions
- How would you derive the shortcut formula Gain% = Error/(True - Error) x 100 for the same-false-weight case?
- How does this problem change if the dealer uses different false weights for buying and selling?
- How would you incorporate a stated discount in addition to the false weights?
- How is this related to successive percentage change and false-weight profit problems?
MCQ Practice
1. A dealer professes to sell goods at cost price but uses a weight of 900g for a kg while buying, and 1100g for a kg while selling. His overall gain percentage is?
Buying gain: (1000-900)/900 x 100 = 11.11%. Selling gain: (1100-1000)/1000 x 100 = 10%. Combined: 11.11 + 10 + (11.11)(10)/100 ≈ 22.22%.
2. A dealer buys and sells using the same false weight of 950g per claimed kg, professing to sell at cost price. His gain percentage, using Error/(True-Error) x 100, is?
Error = 1000-950 = 50. Gain% = 50/(1000-50) x 100 = 50/950 x 100 ≈ 5.26%.
3. A dishonest dealer marks up his price by 20% and also uses a false weight that gives only 800g per claimed kg while selling. His overall gain percentage is?
Weight-error gain: (1000-800)/800 x 100 = 25%. Combined with 20% markup: 20 + 25 + (20)(25)/100 = 20 + 25 + 5 = 50%.
Flash Cards
How to combine buying-side and selling-side gains? — Chain them via a + b + ab/100, never simple addition.
Same-false-weight shortcut (claims cost price)? — Gain% = Error / (True weight - Error) x 100.
Base for buying-side false-weight gain? — The claimed (paid-for) amount is the base.
Base for selling-side false-weight gain? — The true (actually delivered) amount is the base.