Marked Price Calculation: Equal Commissions
The problem asks for the marked price ($M$) of an object given information about two sales scenarios involving different discounts and commission rates, where the final commission amounts are equal.
Setting Up the Equations
Let $M$ represent the marked price of the object.
- Salesperson A:
- Selling Price ($S_A$): Rs. 5 less than marked price, so $S_A = M - 5$.
- Commission Rate: 5% on the selling price.
- Commission Amount ($C_A$): $C_A = 5\% \times S_A = 0.05 \times (M - 5)$.
- Salesperson B:
- Selling Price ($S_B$): Rs. 15 less than marked price, so $S_B = M - 15$.
- Commission Rate: 15% on the selling price.
- Commission Amount ($C_B$): $C_B = 15\% \times S_B = 0.15 \times (M - 15)$.
- Condition: The commission amounts are equal, $C_A = C_B$.
Solving for Marked Price
Equate the commission amounts:
$0.05 \times (M - 5) = 0.15 \times (M - 15)$To simplify, divide both sides by 0.05:
$(M - 5) = \frac{0.15}{0.05} \times (M - 15)$ $(M - 5) = 3 \times (M - 15)$Distribute the 3 on the right side:
$M - 5 = 3M - 45$Rearrange the terms to solve for $M$:
$45 - 5 = 3M - M$ $40 = 2M$ $M = \frac{40}{2}$ $M = 20$Conclusion
The marked price of the object is Rs. 20.
Important Questions from Profit & Loss (Notes)
- A person incurs a loss of 10% by selling a watch for Rs. 450. At what price should the watch be sold to earn 10% profit?
- A shopkeeper bought an item for ₹7825 and marked it at 30% higher than the cost price. If he sells the item by allowing 20% discount, then his profit percentage will be :
- A bought an article at a certain price and sold it at 10% profit. B bought the same article at a price 10% lesser than A and sold it at ₹18 lesser than A. B's gain percentage in this deal is 20%. At what price B bought the article?
- A dealer buys two articles X and Y for ₹500 each. He marks each of them at the same price. He sells X by giving two successive discounts of 50% and 28% and still earns ₹958 as profit. If he sells Y at a single discount of 77%, then what is the profit percentage on Y?
- A shopkeeper earned a profit (in ₹) by selling an item, which is three times the discount offered (in ₹). If the discount offered is 6.25%, what is his profit percentage ?
