A man sells an article for Rs. 480, gaining 20%. What was the ... | Mathematics MCQ | Examoogle

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A man sells an article for Rs. 480, gaining 20%. What was the cost price of the article?

$\text{Rs. } 380$

$\text{Rs. } 400$

$\text{Rs. } 420$

$\text{Rs. } 440$

Correct Answer

⚙️ TE • Technical Direct FormulaMathematicsProfit and Loss

Option B

$\text{Rs. } 400$

Quick Summary:

Use the ratio method: 20% gain means the CP to SP ratio is $5:6$ . Since $6$ parts equals $480$ , $1$ part is $80$ , making the $5$ parts for CP equal to $5 \times 80 = 400$ .

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📐MAMath SolutionDirect Formula

📋 Given

Selling Price (SP) = Rs. 480, Gain Percentage = 20%

🔢 Formula Used

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

⚡ Exam Hall Shortcut / Speed Trick

Use the ratio method: 20% gain means the CP to SP ratio is $5:6$ . Since $6$ parts equals $480$ , $1$ part is $80$ , making the $5$ parts for CP equal to $5 \times 80 = 400$ .

⚠️ Common Student Trap / Pitfall

Students often incorrectly calculate 20% of the Selling Price (subtracting 20% of 480) instead of computing it relative to the Cost Price.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Identify Given Parameters

Note the given selling price and gain percentage from the question: $SP = 480$ and $\text{Gain}\% = 20\%$ .

SP=480,Gain%=20%SP = 480, \quad \text{Gain}\% = 20\%SP=480,Gain%=20%

Apply Cost Price Formula

The formula relating Selling Price and Cost Price during a profit is $CP = \frac{SP \times 100}{100 + \text{Gain}\%}$ .

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

Compute the Cost Price

Substitute the known values into the formula to evaluate the final cost price.

CP=480×100100+20=48000120=400CP = \frac{480 \times 100}{100 + 20} = \frac{48000}{120} = 400CP=100+20480×100​=12048000​=400

✅

B is correct because the calculated cost price of the article is Rs. 400.

Core Concepts Used

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Cost Price and Selling Price Profit and Loss Percentage Ratio Method

💡 EXAM TIP

Mastering percentage-based scaling and ratios helps efficiently solve discount, markup, and mixture problems in quantitative aptitude.

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