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?
Two bikes were sold for a total of ₹ $1,50,000$. One bike was sold at $33\frac{1}{3}\%$ loss and the other at $20\%$ profit. The cost price of the first bike is equal to the selling price of the other bike. Find the over all loss.
What will be the profit percentage on selling an article at a certain price if there is $30\%$ loss on selling the article at $\frac{3}{5}$ of the selling price?
- 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?
