Step 1: Understanding the Concept:
This problem deals with the relationship between three price points: Cost Price (CP), Selling Price (SP), and Marked Price (MP).
1. Discount is always calculated on the Marked Price (MP) to arrive at the Selling Price (SP).
2. Profit (or Gain) is always calculated on the Cost Price (CP) to arrive at the Selling Price (SP).
By equating these two expressions for SP, we can find the unknown Cost Price.
Step 2: Key Formula or Approach:
A highly efficient direct formula for such problems is the CP-MP ratio:
\[ \frac{CP}{MP} = \frac{100 - \text{Discount%}}{100 + \text{Profit%}} \]
Alternatively, one can find SP first and then CP.
Step 3: Detailed Explanation:
Given data:
Marked Price (MP) = Rs. 2500
Discount percentage (D%) = 10%
Profit percentage (P%) = 8%
Let's use the direct ratio method:
\[ \frac{CP}{2500} = \frac{100 - 10}{100 + 8} \]
\[ \frac{CP}{2500} = \frac{90}{108} \]
Simplifying the fraction \( \frac{90}{108} \) by dividing both numerator and denominator by their common factor, 18:
\[ 90 \div 18 = 5 \]
\[ 108 \div 18 = 6 \]
So, \( \frac{CP}{2500} = \frac{5}{6} \).
Now, solve for CP by cross-multiplication:
\[ CP = 2500 \times \frac{5}{6} \]
\[ CP = \frac{12500}{6} \]
Dividing 12500 by 6:
1. \( 12 \div 6 = 2 \)
2. \( 5 \div 6 = 0 \), remainder 5
3. \( 50 \div 6 = 8 \), remainder 2
4. \( 20 \div 6 = 3 \), remainder 2
5. \( 20 \div 6 = 3 \), and so on.
\[ CP \approx 2083.333... \]
Rounding to the nearest two decimal places, we get Rs. 2083.33.
Step 4: Final Answer:
The cost price of the article is Rs. 2083.33.