A shopkeeper sells an item for Rs. 840, thereby gaining 20%. W... | Mathematics MCQ | Examoogle

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A shopkeeper sells an item for Rs. 840, thereby gaining 20%. What was the cost price of the item?

$\text{Rs. } 672$

$\text{Rs. } 700$

$\text{Rs. } 720$

$\text{Rs. } 750$

Correct Answer

📐 MA • Math Ratio MethodMathematicsMathematics

Option B

$\text{Rs. } 700$

Quick Summary:

20% gain means SP is 120% of CP, or ratio $CP: SP = 5: 6$ . So $6 \text{ units} = 840 \implies 1 \text{ unit} = 140 \implies 5 \text{ units} = 5 \times 140 = 700$ .

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📐MAMath SolutionRatio Method

📋 Given

Selling Price (SP) = Rs. 840, Gain Percentage = 20%

🔢 Formula Used

Cost Price (CP)=Selling Price (SP)1+Gain%100\text{Cost Price (CP)} = \frac{\text{Selling Price (SP)}}{1 + \frac{\text{Gain\%}}{100}}Cost Price (CP)=1+100Gain%​Selling Price (SP)​

⚡ Exam Hall Shortcut / Speed Trick

20% gain means SP is 120% of CP, or ratio $CP: SP = 5: 6$ . So $6 \text{ units} = 840 \implies 1 \text{ unit} = 140 \implies 5 \text{ units} = 5 \times 140 = 700$ .

⚠️ Common Student Trap / Pitfall

Calculating 20% directly on the Selling Price ( $840 \times 0.20 = 168$ ) and subtracting it ( $840 - 168 = 672$ ), which yields Option A incorrectly.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Identify Given Parameters

Note the selling price $SP = \text{Rs. } 840$ and the gain percentage $\text{Gain\%} = 20\%$ .

SP=Rs. 840,Gain%=20%SP = \text{Rs. } 840, \quad \text{Gain\%} = 20\%SP=Rs. 840,Gain%=20%

Apply Cost Price Formula

Use the standard relation between Cost Price ( $CP$ ), Selling Price ( $SP$ ), and Gain Percentage.

CP=100100+Gain%×SPCP = \frac{100}{100 + \text{Gain\%}} \times SPCP=100+Gain%100​×SP

Substitute and Calculate

Substitute $SP = 840$ and $\text{Gain\%} = 20$ into the formula to find $CP$ .

CP=100120×840=56×840=Rs. 700CP = \frac{100}{120} \times 840 = \frac{5}{6} \times 840 = \text{Rs. } 700CP=120100​×840=65​×840=Rs. 700

Verify Result

Check if 20% gain on Rs. 700 gives Rs. 840: $700 + (0.20 \times 700) = 700 + 140 = 840$ . This matches the option.

CP=Rs. 700CP = \text{Rs. } 700CP=Rs. 700

✅

B is correct because calculating the Cost Price gives $\frac{100}{120} \times 840 = \text{Rs. } 700$ , matching Option B.

Core Concepts Used

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Cost Price and Selling Price Profit Percentage Calculation Fractional Ratio Method in Commercial Math

💡 EXAM TIP

Percentage markup/discount problems follow the same multiplicative factor model: $SP = CP \times (1 + \frac{P}{100})$ , which is mathematically identical to successive percentage changes and compound interest factors.

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