A shopkeeper sells an item for Rs. 840 and incurs a loss of 16... | Mathematics MCQ | Examoogle

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A shopkeeper sells an item for Rs. 840 and incurs a loss of 16%. At what price should he sell it to gain 8%?

$\text{Rs. } 1080$

$\text{Rs. } 1120$

$\text{Rs. } 960$

$\text{Rs. } 1050$

Correct Answer

📐 MA • Math Proportion FormulaMathematicsMathematics

Option A

$\text{Rs. } 1080$

Quick Summary:

Use the direct relation $\frac{ \text{SP}_1}{100 - \text{Loss}\%}\%$ = $\frac{ \text{SP}_2}{100 + \text{Profit}\%}\%$ to bypass finding the cost price and solve in a single step.

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📐MAMath SolutionProportion Formula

📋 Given

Selling price = Rs. 840, Loss percentage = 16%, Desired profit percentage = 8%

🔢 Formula Used

SP2=SP1imes100+extProfit%100−extLoss%\text{SP}_2 = \text{SP}_1 imes \frac{100 + ext{\text{Profit}}\%}{100 - ext{\text{Loss}}\%}SP2​=SP1​imes100−extLoss%100+extProfit%​

⚡ Exam Hall Shortcut / Speed Trick

Use the direct relation $\frac{\text{SP}_1}{100 - \text{Loss}\%}\%$ = $\frac{\text{SP}_2}{100 + \text{Profit}\%}\%$ to bypass finding the cost price and solve in a single step.

⚠️ Common Student Trap / Pitfall

Students frequently calculate the percentage values directly on the given selling price rather than finding the cost price first.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Identify Given Data

Note down the initial selling price $SP_1 = \text{Rs. } 840$ and the loss percentage of $16\%$ .

SP1=840,extLoss=16%\text{SP}_1 = 840, ext{\text{Loss}} = 16\%SP1​=840,extLoss=16%

Calculate Cost Price

Determine the cost price ( $CP$ ) using the formula $CP = \frac{SP_1}{1 - \text{Loss}\%}$ .

CP=8400.84=1000CP = \frac{840}{0.84} = 1000CP=0.84840​=1000

Calculate Target Selling Price

Apply the desired $8\%$ profit percentage to the cost price to find the new selling price $SP_2$ .

SP2=1000imes1.08=1080\text{SP}_2 = 1000 imes 1.08 = 1080SP2​=1000imes1.08=1080

✅

A is correct because selling the item for Rs. 1080 results in an 8% profit over the calculated cost price of Rs. 1000.

Core Concepts Used

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Cost Price and Selling Price Profit and Loss Percentages Direct Proportion Formulas

💡 EXAM TIP

Mastering these percentage scaling shortcuts helps quickly solve complex discount and markup problems in quantitative aptitude sections.

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