Practice Questions
Concept Explanation
A dishonest dealer uses a weight that measures less than the standard (false weight) but charges for the standard weight, or mixes this with a stated profit%.
Effective gain% when false weight w is used instead of true weight W:
Gain% = ((W − w) / w) × 100 on the weight used.
If he also claims x% profit on CP, combine using multiplier method for placement speed.
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Q1 EasyA shopkeeper uses 900 gm weight for 1 kg. His gain percent is:ExplanationHe charges for 1000 g but delivers 900 g. Gain% = ((1000 − 900)/900) × 100 = 100/900 × 100 = 11 1/9%.
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Q2 EasyBy using 975 gm instead of 1 kg, a shopkeeper gains:ExplanationGain% = ((1000 − 975)/975) × 100 = 25/975 × 100 = 2 4/13% ≈ 2.56%.
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Q3 EasyA provision store uses a weight of 980 gm for 1 kg while selling goods at cost price. What is the shopkeeper's gain percent from the false weight?ExplanationGain% = ((1000 − 980)/980) × 100 = 20/980 × 100 = 2 1/49% ≈ 2.04%.
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Q4 EasyA dishonest merchant delivers 880 gm of rice while charging the customer for 1 kg at cost price. What is his gain percent from the false weight?ExplanationGain% = ((1000 − 880)/880) × 100 = 120/880 × 100 = 13 7/11% ≈ 13.64%.
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Q5 MediumA dishonest dealer professes to sell his goods at cost price, but uses a weight of 960 gm for the kg weight. Find his gain percent.ExplanationGain% = ((1000 − 960)/960) × 100 = 40/960 × 100 = 4 1/6% ≈ 4.17%.
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Q6 MediumA shopkeeper sells his goods at cost price but uses a weight of 850 gm for a kilogram. Find his gain percent.ExplanationGain% = ((1000 − 850)/850) × 100 = 150/850 × 100 = 17 11/17% ≈ 17.65%.
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Q7 MediumA dishonest fruit vendor uses a weight of 800 gm while charging customers for 1 kg of apples at the cost price. What is his gain percent from the false weight alone?ExplanationGain% = ((1000 − 800)/800) × 100 = 200/800 × 100 = 25%.
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Q8 MediumA dealer professes to sell sugar at cost price but uses 950 gm weight for every 1 kg sold to customers. What is his gain percent from the short weight?ExplanationGain% = ((1000 − 950)/950) × 100 = 50/950 × 100 = 5 5/19% ≈ 5.26%.
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Q9 MediumA shopkeeper uses 900 gm weight for 1 kg and also sells the goods at a profit of 5% on cost price. What is his approximate total gain percent?ExplanationWeight multiplier = 10/9. Total gain = (10/9) × 1.05 − 1 = 1.166... − 1 ≈ 16.7%, closest to 17%.
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Q10 HardA shopkeeper sells goods at a profit of 10% and uses a weight 20% less than the actual weight. His total gain percent is:Explanation20% less weight means 800 g sold for 1000 g → weight gain 25%. Total gain = 1.25 × 1.10 − 1 = 37.5%.
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Q11 HardA grocer sells tea at a profit of 8% and uses a weight of 900 gm instead of 1 kg. His total profit percentage is:ExplanationWeight multiplier = 1000/900 = 10/9. Total = (10/9) × 1.08 − 1 = 1.20 − 1 = 20%.
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Q12 HardA shopkeeper uses 750 gm weight for 1 kg and also declares a profit of 20% on the cost price of the goods. What is his approximate total gain percent?ExplanationWeight gain = (250/750) × 100 = 33⅓%. Total gain = 1.333... × 1.20 − 1 = 60%.
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Q13 HardA retailer uses 920 gm instead of 1 kg and also sells the goods at a profit of 10% on cost price. What is his approximate total gain percent?ExplanationWeight multiplier = 1000/920. Total = (1000/920) × 1.10 − 1 = 1.1956... − 1 ≈ 19.6%, closest to 19%.
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Q14 HardA dealer uses 840 gm weight for 1 kg and also sells the goods at a profit of 10% on cost price. What is his approximate total gain percent?ExplanationWeight gain = (160/840) × 100 = 19.05%. Total = 1.1905 × 1.10 − 1 ≈ 30.95%, closest to 31%.
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DS1 Easy
In a quantitative aptitude drill on dishonest trade practices, candidates must find the gain percent arising from false weight alone. What is the gain percent from false weight alone?
Statement IThe shopkeeper uses 900 gm weight instead of the standard 1 kg weight.
Statement IIThe goods are sold at cost price with no declared profit.
ExplanationStatement I alone fixes the false weight ratio. Gain% = ((1000 − 900)/900) × 100 = 11 1/9%. Statement II confirms no extra declared profit. -
DS2 Medium
What is the total gain percent on cost price?
Statement IThe false weight used gives an extra gain of 10% on cost price.
Statement IIThe dealer also charges a further 5% profit on cost price over and above the weight gain.
ExplanationTotal multiplier = 1.10 × 1.05 = 1.155 → 15.5% total gain. Both the weight gain and declared profit are needed.
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DS3 Medium
A quality-control audit reviews whether the gain from using a short weight alone exceeds 20%. Is the gain percent from false weight alone greater than 20%?
Statement IThe dealer uses 800 gm weight while charging for 1 kg.
Statement IIThe dealer also adds a declared profit of 10% on cost price.
ExplanationStatement I: Weight gain = (200/800) × 100 = 25%, which exceeds 20%. Statement II adds declared profit but is not needed to answer about weight gain alone. -
DS4 Hard
An investigative worksheet asks how much material is actually delivered when a shopkeeper uses a false weight. What weight is actually delivered per 1 kg charged to the customer?
Statement IThe gain percent from false weight alone is 5%.
Statement IIThe standard weight charged to the customer is 1 kg (1000 gm).
ExplanationGain% = ((1000 − w)/w) × 100 = 5 → 1000 − w = 0.05w → w = 1000/1.05 ≈ 952.38 gm. Both the gain rate and standard charged weight are needed.