UPSC Prelims 2005 Q96: Science & Technology – Quantitative Aptitude
Left pan of a faulty balance weighs 100 gram more than its right pan. A shopkeeper keeps
the weight measure in the left pan while buying goods but keeps it in the right pan while selling
his goods. He uses only 1 kg weight measure. If he sells his goods at the listed cost price, what is
his gain?
- (a) 200/11 %
- (b) 100/11 %
- (c) 100/9 %
- (d) 200/9 %
Answer: (d) 200/9 %
Explanation
Faulty balance: shopkeeper's gain
| Step | Result |
|---|---|
| Buying (1 kg weight in the left pan, goods in the right) | Goods weigh 1100 g for a 1 kg weight |
| Selling (1 kg weight in the right pan, goods in the left) | Goods weigh 900 g for a 1 kg weight |
| Per 900 g sold | He charges for 1000 g, so for 1100 g he realises 1222.2 g worth |
| Gain | (1222.2 - 1000) / 1000 = 22.2% = 200/9 % |
Buying 1100 g at the price of 1000 g and selling at the listed price by giving only 900 g for each 1000 g worth gives a gain of 200/9 %.
Answer: (d) 200/9 %.
Why each option is right or wrong
- (a) Incorrect. 200/11 % divides by the revenue, not the cost.
- (b) Incorrect. 100/11 % comes from using the wrong weights.
- (c) Incorrect. 100/9 % uses half of the actual excess.
- (d) CORRECT. The gain is 200/9 % on the cost.
Key point
Heavy left pan: buying gets 1100 g, selling gives 900 g, gain 200/9 %.
Remember
The shopkeeper gains 200/9 percent with the faulty balance.
Common mistakes
- Dividing the gain by the selling value instead of the cost.
- Adding 100 g once instead of at both ends.
- Swapping which pan holds the goods when buying.
Exam tip
Write the actual weights for both transactions, then compare to 1000 g.
Sources
- R. S. Aggarwal — Quantitative Aptitude for Competitive Examinations (Profit and Loss)
- Arun Sharma — How to Prepare for Quantitative Aptitude for the CAT (Profit and Loss)