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A dishonest dealer professes to sell his goods at cost price, but he uses a weight of 970 grams for a kg weight. Find his gain percentage.

  • A.\(7\frac{19}{87}\%\)
  • B.\(6\frac{9}{87}\%\)
  • C.\(3\frac{9}{97}\%\)
  • D.\(6\frac{9}{77}\%\)

Answer: C

His gain is 3 9/97 %.

He sells 970 g as 1000 g, so the goods that cost him for 970 g are sold for the price of 1000 g. The gain is the 30 g difference on the 970 g.

\[ \frac{30}{970}\times100=\frac{300}{97}=3\frac{9}{97}\% \]

The other options are not equal to 300/97.

This is a common result: when a dealer uses a false weight, the gain percentage is (error / true weight used) × 100. Here the error is 30 g and the weight actually given is 970 g, which gives 3 9/97%. Using 1000 g as the base would give 3%, which is not an option.

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