Dishonest Shopkeeper: False Weight Profit and Questions
Dishonest Shopkeeper questions deal with false weights, short measures and incorrect quantities. A seller may charge for a full quantity but give less, creating an effective profit even at cost price. The key calculation compares the quantity charged for with the quantity actually supplied. This page covers formulas, cases, shortcuts and numerical examples.
What Is a Dishonest Shopkeeper Problem?
If a shopkeeper charges the price of Q units but supplies q units, and the cost per unit is C, then the actual cost is qC. If the amount collected is S, the actual profit percentage is ((S - qC) / qC) × 100. When the seller charges at cost price, S = QC, so profit percentage = ((Q - q) / q) × 100.
Dishonest Shopkeeper Formula & Tricks
Important Formulas
Q is the quantity charged for and q is the quantity actually supplied. The actual cost is based on q, so q is the denominator.
If the shopkeeper gives x% less than the stated quantity, the supplied quantity is (100 − x)% of the stated quantity.
Here p% is the profit claimed on the stated quantity, Q is the charged quantity and q is the quantity actually supplied. This assumes the cost per unit remains constant.
If the shopkeeper charges cost price and earns r% actual profit, q is the quantity supplied against Q units charged.
Quick Tricks
In false-weight questions, profit is calculated on the actual cost of the quantity supplied. Therefore, divide the shortage by the quantity supplied, not by the quantity charged for.
If x% less quantity is supplied, use x/(100 − x) × 100 for the profit percentage when the price charged is the cost price of the stated quantity.
Convert kilograms to grams or litres to millilitres before applying the formula. The ratio must use the same unit for both quantities.
Dishonest Shopkeeper Concepts
False Weight at Cost Price
The amount received equals the cost of Q units, while the actual cost is the cost of q units. Hence, profit = cost of (Q − q) units. For 1 kg charged and 800 g supplied, profit = (1000 − 800)/800 × 100 = 25%.
Supplying a Specified Percentage Less
The shortage is x parts, but the cost is incurred only for 100 − x parts. This is why x% less quantity does not produce only x% profit.
False Weight Along with Stated Profit
Take the cost per unit as C. The amount collected is (1 + p/100)QC, while the actual cost is qC. Cancelling C gives the formula. If q = Q, it reduces to the stated p% profit.
Finding the False Weight from Actual Profit
From r = (Q − q)/q × 100, we get q(100 + r) = 100Q. Thus, the false quantity can be found directly from the actual profit percentage.
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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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Dishonest Shopkeeper Revision Points
Use these rules for false-weight and short-measure calculations.
- At cost price, profit % = (charged quantity − supplied quantity)/supplied quantity × 100.
- If x% less quantity is supplied, profit % = x/(100 − x) × 100.
- For 1 kg charged and 900 g supplied, the profit is 11 1/9%, not 10%.
- Use identical units, such as grams with grams or millilitres with millilitres.
- With a stated p% profit and false quantity q for Q charged, actual profit % = [(1 + p/100)Q/q − 1] × 100.
- For r% actual profit at cost price, supplied quantity = 100Q/(100 + r).
Dishonest Shopkeeper FAQs
What is the dishonest shopkeeper formula when 1 kg is charged but 900 g is given?
Profit % = (1000 − 900)/900 × 100 = 100/9% = 11 1/9%.
A shopkeeper gives 20% less quantity at cost price. What is his profit?
The supplied quantity is 80% of the stated quantity. Profit = 20/80 × 100 = 25%.
Why is the supplied quantity used as the denominator?
Profit is earned over the actual cost incurred. Since the actual cost relates to the quantity supplied, profit percentage is divided by that quantity.
A shopkeeper charges for 2 kg but gives 1.8 kg at cost price. Find the profit percentage.
Profit = (2 − 1.8)/1.8 × 100 = 0.2/1.8 × 100 = 11 1/9%.
A dishonest shopkeeper gives 800 g for 1 kg and claims a 10% profit. What is the actual profit?
Actual profit = [(1.10 × 1000/800) − 1] × 100 = 37.5%.
How much quantity should be supplied if the shopkeeper wants a 25% profit while charging cost price for 1 kg?
q = 1000 × 100/(100 + 25) = 800 g. Thus, he supplies 800 g.