Calculating Second Person's Gain Percentage
This problem involves calculating successive percentage gains.
Understanding the Gains
Let the original cost price (CP) of the article be '$C$'.
- The first person sold the article at a gain of 15%.
- The total gain on the original price was 38%.
Step 1: Calculate the First Selling Price (SP1)
The first person's selling price ($SP1$) is the original cost price plus the 15% gain.
Using the formula: $SP = CP \times (1 + \frac{\text{Gain}\%}{100})$
$SP1 = C \times (1 + \frac{15}{100}) = C \times (1 + 0.15) = 1.15C$
Step 2: Calculate the Total Selling Price (SP_total)
The total selling price ($SP_{total}$) is the original cost price plus the total gain of 38%.
$SP_{total} = C \times (1 + \frac{38}{100}) = C \times (1 + 0.38) = 1.38C$
Step 3: Calculate the Second Person's Gain
The second person bought the article at $SP1$ (which is $1.15C$) and sold it at $SP_{total}$ (which is $1.38C$).
Second Person's Gain = $SP_{total} - SP1$
Second Person's Gain = $1.38C - 1.15C = 0.23C$
Step 4: Calculate the Second Person's Gain Percentage
The gain percentage for the second person is calculated based on their cost price, which was $SP1$.
Gain Percentage = $\frac{\text{Second Person's Gain}}{\text{Second Person's Cost Price (SP1)}} \times 100$
Gain Percentage = $\frac{0.23C}{1.15C} \times 100$
Gain Percentage = $\frac{0.23}{1.15} \times 100 = \frac{1}{5} \times 100 = 20\%$
Therefore, the gain percentage of the second person was 20%.
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