Question

A trader marks an article \(40%\) above the cost price. He allows two successive discounts of \(10%\) and \(20%\). If the final selling price is ₹1008, then the cost price of the article is:

• A. ₹950
• B. ₹1000
• C. ₹1050
• D. ₹1100

Hint:

Successive discounts are never added directly. Use: \[ \text{Net Multiplier} = (1-d_1)(1-d_2) \] For \(10%\) and \(20%\) discounts: \[ 0.9\times0.8=0.72 \]

Answer 1

The Correct Option is B

Concept: This question combines the concepts of Marked Price, Successive Discounts, and Selling Price. Such questions are frequently asked in CUET GAT because they test conceptual understanding rather than direct formula application. A common mistake made by students is to simply add discounts: \[ 10%+20%=30% \] This is incorrect because successive discounts are applied one after another.

Step 1: Assume the Cost Price. Let the Cost Price be: \[ CP=x \] The article is marked \(40%\) above cost price. Therefore, \[ MP=x+\frac{40}{100}x \] \[ MP=1.4x \]

Step 2: Apply first discount. First discount: \[ 10% \] Remaining price: \[ 90% \] Therefore, \[ Price=1.4x\times 0.9 \] \[ =1.26x \]

Step 3: Apply second discount. Second discount: \[ 20% \] Remaining price: \[ 80% \] Thus: \[ SP=1.26x\times0.8 \] \[ SP=1.008x \]

Step 4: Use the given selling price. Given: \[ SP=1008 \] Therefore, \[ 1.008x=1008 \] \[ x=\frac{1008}{1.008} \] \[ x=1000 \]

Step 5: Verification. Cost Price: \[ 1000 \] Marked Price: \[ 1400 \] After \(10%\) discount: \[ 1400\times0.9=1260 \] After \(20%\) discount: \[ 1260\times0.8=1008 \] The value satisfies the condition.

Step 6: Final conclusion. Hence, \[ \boxed{\text{Cost Price}=₹1000} \] Therefore, \[ \boxed{\text{Option (B)}} \]