The cost price of a watch is 800. What should be the marked pr... | Mathematics MCQ | Examoogle

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The cost price of a watch is 800. What should be the marked price to ensure a 20% profit after allowing a 20% discount?

1000

1200

1250

1100

Correct Answer

⚙️ TE • Technical Ratio MethodMathematicsArithmetic

Option B

1200

Quick Summary:

Use the ratio of CP and MP: $\text{CP}:\text{MP} = (100 - D):(100 + P) = (100-20):(100+20) = 80:120 = 2:3$ . Since $2$ units correspond to 800, $1$ unit = 400, so $3$ units = 1200.

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📐MAMath SolutionRatio Method

📋 Given

Cost Price (CP) = 800, Profit Percent = 20%, Discount Percent = 20%.

🔢 Formula Used

MP=CP×(100+Profit%100−Discount%)\text{MP} = \text{CP} \times \left( \frac{100 + \text{Profit}\%}{100 - \text{Discount}\%} \right)MP=CP×(100−Discount%100+Profit%​)

⚡ Exam Hall Shortcut / Speed Trick

Use the ratio of CP and MP: $\text{CP}:\text{MP} = (100 - D):(100 + P) = (100-20):(100+20) = 80:120 = 2:3$ . Since $2$ units correspond to 800, $1$ unit = 400, so $3$ units = 1200.

⚠️ Common Student Trap / Pitfall

Many students mistakenly apply the 20% discount directly to the cost price or try to add the percentages ( $20\% + 20\% = 40\%$ ) instead of calculating them sequentially.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Define the relationship

The relationship between cost price (CP), marked price (MP), profit (P), and discount (D) is given by equating the selling price (SP) calculated through both perspectives: $\text{SP} = \text{CP} \times (1 + \frac{P}{100})$ and $\text{SP} = \text{MP} \times (1 - \frac{D}{100})$ .

CP×(1+0.20)=MP×(1−0.20)\text{CP} \times (1 + 0.20) = \text{MP} \times (1 - 0.20)CP×(1+0.20)=MP×(1−0.20)

Substitute the values

Substitute $\text{CP} = 800$ , $P = 20\%$ , and $D = 20\%$ into the equation.

800×1.20=MP×0.80800 \times 1.20 = \text{MP} \times 0.80800×1.20=MP×0.80

Calculate MP

Rearrange the equation to isolate MP: $\text{MP} = \frac{800 \times 1.2}{0.8}$ .

MP=9600.8=1200\text{MP} = \frac{960}{0.8} = 1200MP=0.8960​=1200

✅

B is correct because the marked price required to achieve a 20% profit while offering a 20% discount is 1200.

Core Concepts Used

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Profit and Loss Discount Percentages Marked Price calculation

💡 EXAM TIP

This concept is fundamentally linked to 'Successive Percentages' and 'Ratio and Proportion'; always remember that profit is calculated on CP, while discount is calculated on MP.

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