A dishonest dealer defrauds to the extent of x% while purchasing and s...
**Shortcut Method to Calculate Gain Percent on Outlay**
To find the gain percent on the outlay when a dishonest dealer defrauds by a certain percentage while purchasing and selling goods using a faulty weight, we can use the following shortcut method:
**Step 1: Convert Fractions to Percentages**
First, we need to convert the given defrauding percentage (x%) into its equivalent fraction. To convert a percentage to a fraction, divide the given percentage by 100.
For example, if the dealer defrauds by 25%, the equivalent fraction would be 25/100.
**Step 2: Calculate the Overall Frauding Percentage**
The dishonest dealer defrauds both while purchasing and selling goods. Therefore, the overall percentage of defrauding would be the sum of the purchase fraud percentage and the selling fraud percentage.
For example, if the dealer defrauds by 20% while purchasing and 10% while selling, the overall defrauding percentage would be 20% + 10% = 30%.
**Step 3: Use the Gain Percentage Formula**
The gain percent on the outlay can be calculated using the formula:
Gain percent = (Overall Frauding Percentage / (100 + Overall Frauding Percentage)) × 100
For example, if the overall defrauding percentage is 30%, the gain percent on the outlay would be:
Gain percent = (30 / (100 + 30)) × 100 = (30 / 130) × 100 ≈ 23.08%
So, the gain percent on the outlay in this case is approximately 23.08%.
**Example Calculation**
Let's consider an example where the dealer defrauds by 15% while purchasing and 12% while selling.
**Step 1: Convert Fractions to Percentages**
15% = 15/100
12% = 12/100
**Step 2: Calculate the Overall Frauding Percentage**
Overall Frauding Percentage = 15% + 12% = 27%
**Step 3: Use the Gain Percentage Formula**
Gain percent = (27 / (100 + 27)) × 100 = (27 / 127) × 100 ≈ 21.26%
Therefore, the gain percent on the outlay in this case is approximately 21.26%.
Using this shortcut method saves time and helps quickly calculate the gain percent on the outlay when a dishonest dealer defrauds using a faulty weight while purchasing and selling goods.
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