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 a profit of 12%?

$\text{Rs. } 1120$

$\text{Rs. } 1080$

$\text{Rs. } 1150$

$\text{Rs. } 1200$

Correct Answer

📐 MA • Math Ratio MethodMathematicsMathematics

Option A

$\text{Rs. } 1120$

Quick Summary:

Equate the selling price percentages directly: $(100 - 16)\%$ corresponds to Rs. 840, so find $(100 + 12)\%$ directly by multiplying $840 imes \frac{112}{84}$ .

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📐MAMath SolutionRatio Method

📋 Given

Selling Price 1 = Rs. 840, Loss % = 16%, Desired Profit % = 12%

🔢 Formula Used

CP=SPimes100100−extLoss%CP = \frac{SP imes 100}{100 - ext{\text{Loss}}\%}CP=100−extLoss%SPimes100​

⚡ Exam Hall Shortcut / Speed Trick

Equate the selling price percentages directly: $(100 - 16)\%$ corresponds to Rs. 840, so find $(100 + 12)\%$ directly by multiplying $840 imes \frac{112}{84}$ .

⚠️ Common Student Trap / Pitfall

Students often mistakenly calculate 12% profit directly on the given selling price (Rs. 840) instead of finding the Cost Price first.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Find the Cost Price

Since there is a loss of 16%, the selling price is 84% of the cost price. We first find the Cost Price using the formula: $CP = \frac{SP imes 100}{100 - \text{Loss}\%}$ .

CP=840imes100100−16=8400084=1000CP = \frac{840 imes 100}{100 - 16} = \frac{84000}{84} = 1000CP=100−16840imes100​=8484000​=1000

Calculate the Desired Selling Price

To gain a profit of 12%, the new selling price must be 112% of the cost price of Rs. 1000.

SP2=100+extProfit%100imes CP=112100imes1000=1120SP_2 = \frac{100 + ext{\text{Profit}}\%}{100} \text{imes CP} = \frac{112}{100} imes 1000 = 1120SP2​=100100+extProfit%​imes CP=100112​imes1000=1120

✅

A is correct because the calculated new selling price to gain 12% profit is Rs. 1120.

Core Concepts Used

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Cost Price and Selling Price relationship Profit and Loss percentage calculations Unitary method / Ratio approach

💡 EXAM TIP

This proportional percentage comparison technique is widely applicable in discount, markup, and mixture problems across quantitative aptitude tests.

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