Question : A seller uses a faulty weight in place of a 2 kg weight and earns a 25% profit. He claims that he is selling at the cost price in front of the customers but uses a faulty weight. How much error is there in the 2 kg weight to gain 25%?
Option 1: 250 gm
Option 2: 400 gm
Option 3: 500 gm
Option 4: 300 gm
Correct Answer: 400 gm
Solution : Let the error be m gm. Percentage profit = $[\frac{\text{Error}}{\text{(True weight–Error)}}] × 100 $ According to the question, $25 = (\frac{m}{(2000 - m)}) × 100$ $⇒ \frac{25}{100} = \frac{m}{(2000 - m)}$ $⇒ \frac{1}{4} = \frac{m}{(2000 - m)}$ $⇒ 2000 - m = 4m$ $⇒ 5m = 2000$ $⇒ m = \frac{2000}{5} = 400$ gm ∴ The faulty weight used by the seller has the error of 400 gm. Hence, the correct answer is 400 gm.
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