A shopkeeper sells an item at a loss of 12%. If he had sold it... | Mathematics MCQ | Examoogle

MathematicsProfit and Loss

A shopkeeper sells an item at a loss of 12%. If he had sold it for Rs. 180 more, he would have gained 8%. What is the cost price of the item?

$\text{Rs. } 900$

$\text{Rs. } 850$

$\text{Rs. } 1000$

$\text{Rs. } 750$

Correct Answer

⚙️ TE • Technical Direct FormulaMathematicsProfit and Loss

Option A

$\text{Rs. } 900$

Quick Summary:

The total percentage change between a 12% loss and an 8% gain is $12\% + 8\% = 20\%$ . Therefore, $20\%$ of the Cost Price equals Rs. 180, giving $CP = \frac{180}{0.20} = \text{Rs. } 900$ .

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📐MAMath SolutionDirect Formula

📋 Given

Initial loss percentage = 12%, Increased selling price = Rs. 180, New gain percentage = 8%

🔢 Formula Used

CP=Difference in SPSum of profit and loss percentagesimes100CP = \frac{\text{Difference in SP}}{\text{Sum of profit and loss percentages}} imes 100CP=Sum of profit and loss percentagesDifference in SP​imes100

⚡ Exam Hall Shortcut / Speed Trick

The total percentage change between a 12% loss and an 8% gain is $12\% + 8\% = 20\%$ . Therefore, $20\%$ of the Cost Price equals Rs. 180, giving $CP = \frac{180}{0.20} = \text{Rs. } 900$ .

⚠️ Common Student Trap / Pitfall

Students often mistakenly take the difference between the two percentages ( $8\% - (-12\%) = 20\%$ is correct, but subtracting them as $8 - 12 = 4\%$ is a common arithmetic sign error).

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Understand the Selling Prices

Let the Cost Price of the item be $CP$ . Initially, the item is sold at a 12% loss, so the first Selling Price is $SP_1 = CP - 0.12 \text{imes CP} = 0.88 imes CP$ .

SP1=0.88imes CPSP_1 = 0.88 \text{imes CP}SP1​=0.88imes CP

Account for the Increased Selling Price

If the item is sold for Rs. 180 more, the new Selling Price yields an 8% gain, so $SP_2 = CP + 0.08 \text{imes CP} = 1.08 imes CP$ .

SP2=1.08imes CPSP_2 = 1.08 \text{imes CP}SP2​=1.08imes CP

Formulate the Equation

According to the problem, the difference between the two selling prices is Rs. 180: $SP_2 - SP_1 = 180$ . Substituting our expressions gives $1.08 \text{imes CP} - 0.88 \text{imes CP} = 180$ .

1.08imes CP−0.88imes CP=1801.08 \text{imes CP} - 0.88 \text{imes CP} = 1801.08imes CP−0.88imes CP=180

Calculate the Cost Price

Simplifying the equation results in $0.20 \text{imes CP} = 180$ . Solving for $CP$ yields $CP = \frac{180}{0.20} = 900$ .

CP=1800.20=900CP = \frac{180}{0.20} = 900CP=0.20180​=900

✅

A is correct because the cost price of the item calculated is Rs. 900.

Core Concepts Used

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Cost Price and Selling Price relation Profit and Loss percentage calculations Linear equation formation from word problems

💡 EXAM TIP

Similar percentage difference concepts are frequently used in Simple Interest and Compound Interest problems involving differences between rates over time.

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