Salesperson 'A' sells an object at a price Rs. 5 less than the marked price, receiving a commission of 5% on the selling price. The same object is sold by person 'B' at a price Rs.15 less than the marked price, receiving a commission of 15% on the selling price. If both A and B receive the same amount in commission, then what is the marked price of the object?
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Marked Price Problem Analysis
This question involves calculating the original marked price of an object based on information about how two different salespeople, A and B, sell it and receive commissions.
Both salespeople sell the object at a price less than the marked price and earn a commission based on their respective selling prices. The key piece of information is that they both receive the same amount of commission.
Defining Variables
Let's denote the marked price of the object as \( MP \).
- Salesperson A sells the object at a price Rs. 5 less than the marked price.
- Salesperson B sells the object at a price Rs. 15 less than the marked price.
Based on this, we can write the selling price for each salesperson:
- Selling Price for A (\( SP_A \)) = \( MP - 5 \)
- Selling Price for B (\( SP_B \)) = \( MP - 15 \)
Calculating Commission
The commission for each salesperson is a percentage of their selling price:
- Commission for A (\( C_A \)) = 5% of \( SP_A \)
- Commission for B (\( C_B \)) = 15% of \( SP_B \)
We can write these commissions using the selling price expressions:
- \( C_A = 0.05 \times (MP - 5) \)
- \( C_B = 0.15 \times (MP - 15) \)
Equating Commissions
The problem states that both A and B receive the same amount in commission. Therefore, we can set their commission amounts equal to each other:
\( C_A = C_B \)
\( 0.05 \times (MP - 5) = 0.15 \times (MP - 15) \)
Solving for Marked Price
Now we need to solve this equation for \( MP \).
First, distribute the percentages on both sides:
\( 0.05 \times MP - 0.05 \times 5 = 0.15 \times MP - 0.15 \times 15 \)
\( 0.05 MP - 0.25 = 0.15 MP - 2.25 \)
Next, gather the \( MP \) terms on one side and the constant terms on the other side. Subtract \( 0.05 MP \) from both sides and add \( 2.25 \) to both sides:
\( 2.25 - 0.25 = 0.15 MP - 0.05 MP \)
\( 2.00 = 0.10 MP \)
Finally, divide by \( 0.10 \) to find the value of \( MP \):
\( MP = \frac{2.00}{0.10} \)
\( MP = 20 \)
The marked price of the object is Rs. 20.
Verification
Let's check if the commissions are indeed equal when \( MP = 20 \).
- For A: \( SP_A = 20 - 5 = 15 \). \( C_A = 5\% \text{ of } 15 = 0.05 \times 15 = 0.75 \).
- For B: \( SP_B = 20 - 15 = 5 \). \( C_B = 15\% \text{ of } 5 = 0.15 \times 5 = 0.75 \).
Since both \( C_A \) and \( C_B \) are equal to 0.75, our calculated marked price of Rs. 20 is correct.
Important Questions from Discount and MP
The marked price of an article is Rs. 1500. A shopkeeper sells it by giving 20% discount on its marked price. If the cost price of the article is Rs. 991, then his profit (in Rs.) is:
Surbhi sold an article for Rs. 176 after giving 12% discount on its marked price. Had she not given any discount; she would have earned a profit of 25%. What is the cost price (in Rs.) of the article?
The marked price of an article is Rs. 240. A shopkeeper sells it by allowing 18% discount on its marked price and still gains 23%. What is the cost price (in Rs.) of the article?
Three shopkeepers A, B and C marked on an identical article at Rs. 4820. A, B and C sold their article on successive discounts of 20% and 20%; 25% and 15%; 30% and 10% respectively. Which shopkeeper gives the maximum discount and how much (in Rs.)?
Find a single discount percentage equivalent to successive discounts of 10%, 20% and 25%.
