Question

A shopkeeper gives 10% discount on an article marked at Rs.2500 and still gains 8%. The cost price of the article is:

• A. Rs.2000
• B. Rs.2050
• C. Rs.2083.33
• D. Rs.2100

Hint:

To save valuable time during exams, skip computing the selling price entirely! Just use the direct ratio trick: $\frac{CP}{MP} = \frac{100-D}{100+P}$. Here, $\frac{CP}{2500} = \frac{90}{108} = \frac{5}{6}$. Calculating $\frac{5}{6}$ of $2500$ gets you to the answer $2083.33$ in a single quick step!

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
In commercial mathematics, profit or loss is always calculated on the Cost Price (CP), while a discount is always applied to the Marked Price (MP). The final price at which the article is sold after subtracting the discount is the Selling Price (SP). By establishing a direct mathematical relationship between the marked price, discount percentage, profit percentage, and cost price, we can bypass multi-step calculations and find the unknown value efficiently.

Step 2: Key Formula or Approach:
There is a direct and highly reliable ratio formula linking Cost Price ($CP$) and Marked Price ($MP$) when both the discount percentage ($D%$) and profit percentage ($P%$) are known: $$\frac{CP}{MP} = \frac{100 - D%}{100 + P%}$$

Step 3: Detailed Explanation:
Given parameters from the problem: Marked Price ($MP$) = Rs.2500 Discount percentage ($D%$) = $10%$ Profit percentage ($P%$) = $8%$ Substitute these known values directly into the ratio formula: $$\frac{CP}{2500} = \frac{100 - 10}{100 + 8}$$ $$\frac{CP}{2500} = \frac{90}{108}$$ Simplify the fraction $\frac{90}{108}$ by dividing both the numerator and the denominator by their greatest common divisor, 18: $$\frac{CP}{2500} = \frac{5}{6}$$ Now, isolate and solve for $CP$ by cross-multiplying: $$CP = \frac{5}{6} \times 2500$$ $$CP = \frac{12500}{6}$$ $$CP \approx 2083.333...$$ Rounding to two decimal places gives a cost price of Rs.2083.33.

Step 4: Final Answer:
The cost price of the article is Rs.2083.33.