Question : A dishonest trader says to customers that he sells his goods at a cost price, but he uses a false weight and gains 12.5% as profit. How many grams does he use to weight 1 kg?
Option 1: 900 g
Option 2: 880.5 g
Option 3: 850 g
Option 4: 888.8 g
Correct Answer: 888.8 g
Solution :
According to the formula,
$12.5\% = [\frac{\text{Error}}{\text{1000 – Error}}] × 100$
⇒ $\frac{1}{8} = [\frac{\text{Error}}{\text{1000 – Error}}]$
⇒ $8\text{Error} = \text{(1000 – Error)}$
⇒ $\text{8Error + Error} = 1000$
⇒ $9\text{Error} = 1000$
⇒ $\text{Error} = \frac{1000}{9}$
So, the trader gives $1000 - \frac{1000}{9}=\frac{8000}{9}=888.8$ g
Hence, the correct answer is 888.8 g.
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