Question:
A merchant sold a car at 60% of the marked price and obtained a loss of 20%. If the cost price of the car is three times the cost price of the bike, then what should be the selling price of the bike to make a profit of 20%?
A merchant sold a car at 60% of the marked price and obtained a loss of 20%. If the cost price of the car is three times the cost price of the bike, then what should be the selling price of the bike to make a profit of 20%?
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In profit and loss problems with multiple items, it's crucial to establish a common variable to link all the given information. Here, the Marked Price of the car (\(MP_{car}\)) serves as the reference point to express all other values.
Updated On: Oct 2, 2025
- 120% of the Marked Price of the car
- 20% of the Marked Price of the car
- 30% of the Marked Price of the car
- 80% of the Marked Price of the car
- 50% of the Marked Price of the car
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
This problem involves concepts of Cost Price (CP), Marked Price (MP), Selling Price (SP), Profit, and Loss. The key is to establish relationships between these variables for both the car and the bike and then express the final required value in terms of the car's marked price.
Step 2: Key Formula or Approach:
SP = MP $\times$ (1 - Discount %)
SP = CP $\times$ (1 - Loss %)
SP = CP $\times$ (1 + Profit %)
Step 3: Detailed Explanation:
Let \(MP_{car}\) and \(CP_{car}\) be the marked price and cost price of the car, respectively.
Let \(CP_{bike}\) and \(SP_{bike}\) be the cost price and selling price of the bike, respectively.
For the car:
The selling price of the car (\(SP_{car}\)) is 60% of its marked price.
\[ SP_{car} = 0.60 \times MP_{car} \] The merchant incurred a loss of 20% on the car.
\[ SP_{car} = CP_{car} \times (1 - 0.20) = 0.80 \times CP_{car} \] Equating the two expressions for \(SP_{car}\):
\[ 0.60 \times MP_{car} = 0.80 \times CP_{car} \] This gives us a relationship between the cost price and marked price of the car:
\[ CP_{car} = \frac{0.60}{0.80} \times MP_{car} = \frac{3}{4} \times MP_{car} = 0.75 \times MP_{car} \] For the bike:
The cost price of the car is three times the cost price of the bike.
\[ CP_{car} = 3 \times CP_{bike} \implies CP_{bike} = \frac{CP_{car}}{3} \] Substituting the expression for \(CP_{car}\) in terms of \(MP_{car}\):
\[ CP_{bike} = \frac{0.75 \times MP_{car}}{3} = 0.25 \times MP_{car} \] The merchant wants to make a profit of 20% on the bike.
\[ SP_{bike} = CP_{bike} \times (1 + 0.20) = 1.20 \times CP_{bike} \] Now, substitute the value of \(CP_{bike}\) in terms of \(MP_{car}\):
\[ SP_{bike} = 1.20 \times (0.25 \times MP_{car}) \] \[ SP_{bike} = 0.30 \times MP_{car} \] Step 4: Final Answer:
The selling price of the bike should be 0.30 times the marked price of the car, which is 30% of the Marked Price of the car.
This problem involves concepts of Cost Price (CP), Marked Price (MP), Selling Price (SP), Profit, and Loss. The key is to establish relationships between these variables for both the car and the bike and then express the final required value in terms of the car's marked price.
Step 2: Key Formula or Approach:
SP = MP $\times$ (1 - Discount %)
SP = CP $\times$ (1 - Loss %)
SP = CP $\times$ (1 + Profit %)
Step 3: Detailed Explanation:
Let \(MP_{car}\) and \(CP_{car}\) be the marked price and cost price of the car, respectively.
Let \(CP_{bike}\) and \(SP_{bike}\) be the cost price and selling price of the bike, respectively.
For the car:
The selling price of the car (\(SP_{car}\)) is 60% of its marked price.
\[ SP_{car} = 0.60 \times MP_{car} \] The merchant incurred a loss of 20% on the car.
\[ SP_{car} = CP_{car} \times (1 - 0.20) = 0.80 \times CP_{car} \] Equating the two expressions for \(SP_{car}\):
\[ 0.60 \times MP_{car} = 0.80 \times CP_{car} \] This gives us a relationship between the cost price and marked price of the car:
\[ CP_{car} = \frac{0.60}{0.80} \times MP_{car} = \frac{3}{4} \times MP_{car} = 0.75 \times MP_{car} \] For the bike:
The cost price of the car is three times the cost price of the bike.
\[ CP_{car} = 3 \times CP_{bike} \implies CP_{bike} = \frac{CP_{car}}{3} \] Substituting the expression for \(CP_{car}\) in terms of \(MP_{car}\):
\[ CP_{bike} = \frac{0.75 \times MP_{car}}{3} = 0.25 \times MP_{car} \] The merchant wants to make a profit of 20% on the bike.
\[ SP_{bike} = CP_{bike} \times (1 + 0.20) = 1.20 \times CP_{bike} \] Now, substitute the value of \(CP_{bike}\) in terms of \(MP_{car}\):
\[ SP_{bike} = 1.20 \times (0.25 \times MP_{car}) \] \[ SP_{bike} = 0.30 \times MP_{car} \] Step 4: Final Answer:
The selling price of the bike should be 0.30 times the marked price of the car, which is 30% of the Marked Price of the car.
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