Question

A trader marks an article 40% above cost price and gives two successive discounts of 10% and 5%. If the selling price is Rs.3591, the cost price of the article is

• A. Rs. 3000
• B. Rs. 4000
• C. Rs. 2000
• D. Rs. 5000

Hint:

To estimate, calculate the net profit or loss percentage:
A markup of \(+40\%\) followed by discounts of \(-10\%\) and \(-5\%\) gives a net multiplier of \(1.4 \times 0.9 \times 0.95 = 1.197\).
This represents a \(19.7\%\) net profit.
Since \(SP = 3591\), the CP must be around \(3591 \div 1.2 = 3000\), which matches Option (A) perfectly.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
This question tests concepts of commercial mathematics involving Cost Price (CP), Marked Price (MP), Selling Price (SP), mark-up percentages, and successive discounts.

Step 2: Key Formulas and approach:
Let the Cost Price of the article be \(C\).
1. Marked Price (MP) after a \(40\%\) markup is:
\[ MP = C \times \left(1 + \frac{40}{100}\right) = 1.4C \] 2. Selling Price (SP) after successive discounts of \(10\%\) and \(5\%\) on the MP is:
\[ SP = MP \times \left(1 - \frac{10}{100}\right) \times \left(1 - \frac{5}{100}\right) \] We are given \(SP = 3591\). We will substitute this value to solve for \(C\).

Step 3: Detailed Explanation:

• Express the Selling Price equation in terms of \(C\):
\[ 3591 = 1.4C \times 0.90 \times 0.95 \]

• Simplify the multipliers:
\[ 1.4 \times 0.90 = 1.26 \] \[ 1.26 \times 0.95 = 1.197 \]

• Substitute these back into the equation:
\[ 3591 = 1.197C \]

• Solve for \(C\) by dividing both sides:
\[ C = \frac{3591}{1.197} \]

• To simplify the division, multiply numerator and denominator by 1000:
\[ C = \frac{3591000}{1197} \]

• Notice that \(1197 \times 3 = 3591\). Therefore:
\[ C = 3000 \]

Step 4: Final Answer:
The cost price of the article is \(\text{Rs. } 3000\), making Option (A) the correct choice.