By selling an article at $\frac{2}{5}$ of its actual selling p... | Mathematics MCQ | Examoogle

MathematicsPrevious Year Paper 2024

By selling an article at $\frac{2}{5}$ of its actual selling price, Ramesh incurs a loss of 16%. If he sells it at 86% of its actual selling price, then the profit percentage is:

82.6%

83.4%

80.6%

81.8%

Correct Answer

📐 MA • Math Ratio MethodMathematicsPrevious Year Paper 2024

Option C

80.6%

Quick Summary:

Let actual SP = 100. Then 2/5 of SP = 40. At 40, loss is 16%, so $CP = 40 / 0.84 = 47.619$ . Then new SP = 86. Profit = (86 - 47.619) / 47.619 * 100 = 80.6%.

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📐MAMath SolutionRatio Method

📋 Given

Selling an article at 2/5 of actual selling price (SP) results in a 16% loss. The goal is to find the profit percentage when sold at 86% of the actual SP.

🔢 Formula Used

CP=SPnew×100100−Loss%=SPnew×100100+Profit%CP = \frac{SP_{new} \times 100}{100 - \text{Loss}\%} = \frac{SP_{new} \times 100}{100 + \text{Profit}\%}CP=100−Loss%SPnew​×100​=100+Profit%SPnew​×100​

⚡ Exam Hall Shortcut / Speed Trick

Let actual SP = 100. Then 2/5 of SP = 40. At 40, loss is 16%, so $CP = 40 / 0.84 = 47.619$ . Then new SP = 86. Profit = (86 - 47.619) / 47.619 * 100 = 80.6%.

⚠️ Common Student Trap / Pitfall

Students often assume the 16% loss applies to the original SP directly, forgetting that the 16% loss is tied to the modified SP of 2/5.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Define variables

Let the actual selling price be $S$ . When sold at $\frac{2}{5}S$ , the loss is $16\%$ . This means the selling price is $84\%$ of the cost price ( $CP$ ).

25S=0.84×CP\frac{2}{5}S = 0.84 \times CP52​S=0.84×CP

Calculate Cost Price

Solve for $CP$ in terms of $S$ . Dividing by $0.84$ gives $CP = \frac{0.4S}{0.84} = \frac{40S}{84} = \frac{10}{21}S$ .

CP=1021SCP = \frac{10}{21}SCP=2110​S

Calculate Profit at new selling price

The new selling price is $86\%$ of $S$ , which is $0.86S = \frac{86}{100}S = \frac{43}{50}S$ . The profit is $(\text{New SP} - CP)$ .

Profit%=(4350S−1021S1021S)×100\text{Profit}\% = \left( \frac{\frac{43}{50}S - \frac{10}{21}S}{\frac{10}{21}S} \right) \times 100Profit%=(2110​S5043​S−2110​S​)×100

Final Calculation

Simplifying the expression: $(\frac{903 - 500}{1050}) / (10/21) \times 100 = (403/1050) \times (21/10) \times 100 = (403/500) \times 100 = 403 / 5 = 80.6\%$ .

80.6%80.6\%80.6%

✅

C is correct because the calculation yields exactly 80.6% profit when selling at 86% of the original selling price.

Core Concepts Used

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Profit and Loss Percentage Calculations Fractional Analysis

💡 EXAM TIP

This concept of 'Ratio of SP' is frequently tested in Ratios and Proportions chapters as well as Arithmetic Progression based profit problems.

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