Ram sells a suitcase to Mohan at a 20% profit. Mohan sells it to Shyam at a 40% profit. If Shyam pays Rs. 1,430 for it, then the price at which Ram bought it is:
Rs. 851.19
Calculating Initial Price with Successive Profits
This problem involves calculating the original cost price of an item after it has been sold multiple times with different profit percentages applied in each transaction. We need to work backward from the final price paid by Shyam to find the initial price at which Ram bought the suitcase.
Understanding the Transactions
Let's break down the transactions:
- Ram sells the suitcase to Mohan at a 20% profit.
- Mohan sells the suitcase to Shyam at a 40% profit.
- Shyam pays Rs. 1,430 for the suitcase.
Step-by-Step Calculation
We can denote the prices at each stage:
- Let \(C_R\) be the cost price for Ram (the price Ram bought it for).
- The selling price for Ram (\(S_R\)) is the cost price for Mohan (\(C_M\)).
- The selling price for Mohan (\(S_M\)) is the cost price for Shyam (\(C_S\)).
Transaction 1: Ram to Mohan
Ram sells to Mohan at a 20% profit. This means Mohan's cost price is Ram's cost price plus 20% of Ram's cost price.
\(C_M = C_R + 20\% \text{ of } C_R\)
In terms of percentage, this is 100% (original price) + 20% (profit) = 120% of \(C_R\).
So, \(C_M = C_R \times \left(1 + \frac{20}{100}\right) = C_R \times 1.20\)
Transaction 2: Mohan to Shyam
Mohan sells to Shyam at a 40% profit. This means Shyam's cost price is Mohan's cost price plus 40% of Mohan's cost price.
\(C_S = C_M + 40\% \text{ of } C_M\)
In terms of percentage, this is 100% (Mohan's price) + 40% (profit) = 140% of \(C_M\).
So, \(C_S = C_M \times \left(1 + \frac{40}{100}\right) = C_M \times 1.40\)
Relating Shyam's Price to Ram's Price
We know \(C_S = 1.40 \times C_M\) and \(C_M = 1.20 \times C_R\).
Substitute the expression for \(C_M\) into the equation for \(C_S\):
\(C_S = 1.40 \times (1.20 \times C_R)\)
\(C_S = (1.40 \times 1.20) \times C_R\)
\(C_S = 1.68 \times C_R\)
Solving for Ram's Cost Price (\(C_R\))
We are given that Shyam pays Rs. 1,430, which means \(C_S = 1430\).
\(1430 = 1.68 \times C_R\)
To find \(C_R\), divide 1430 by 1.68:
\(C_R = \frac{1430}{1.68}\)
Let's perform the division:
\(C_R \approx 851.19047...\)
Rounding this to two decimal places gives approximately Rs. 851.19.
Summary of Calculation Steps
| Step | Description | Formula | Calculation |
|---|---|---|---|
| 1 | Mohan's cost price based on Ram's profit | \(C_M = C_R \times (1 + \text{Profit Rate 1})\) | \(C_M = C_R \times 1.20\) |
| 2 | Shyam's cost price based on Mohan's profit | \(C_S = C_M \times (1 + \text{Profit Rate 2})\) | \(C_S = C_M \times 1.40\) |
| 3 | Substitute \(C_M\) into the equation for \(C_S\) | \(C_S = (1 + \text{Profit Rate 2}) \times (1 + \text{Profit Rate 1}) \times C_R\) | \(C_S = 1.40 \times 1.20 \times C_R = 1.68 \times C_R\) |
| 4 | Solve for \(C_R\) using Shyam's price | \(C_R = \frac{C_S}{(1 + \text{Profit Rate 1}) \times (1 + \text{Profit Rate 2})}\) | \(C_R = \frac{1430}{1.68} \approx 851.19\) |
The price at which Ram bought the suitcase is approximately Rs. 851.19.
Revision Table: Profit Percentage Concepts
| Term | Definition | Formula (Profit) |
|---|---|---|
| Cost Price (CP) | The initial price at which an article is bought. | N/A |
| Selling Price (SP) | The price at which an article is sold. | \(SP = CP + \text{Profit}\) |
| Profit | The gain obtained by selling an article for more than its cost price. | \(SP - CP\) |
| Profit Percentage | Profit expressed as a percentage of the cost price. | \(\left(\frac{\text{Profit}}{CP}\right) \times 100\) |
| SP in terms of CP and Profit % | Selling Price directly calculated from Cost Price and Profit Percentage. | \(SP = CP \times \left(1 + \frac{\text{Profit \%}}{100}\right)\) |
Additional Information: Successive Profit Calculations
When an item is sold and resold with successive profit percentages, the final selling price is calculated by multiplying the original cost price by the successive profit factors. A profit factor for \(x\%\) profit is \(\left(1 + \frac{x}{100}\right)\). If an item is sold with a profit of \(p_1\%\) and then resold with a profit of \(p_2\%\), and the original cost price was CP, the final selling price (which is the final buyer's cost price) is given by:
Final Price \( = CP \times \left(1 + \frac{p_1}{100}\right) \times \left(1 + \frac{p_2}{100}\right)\)
In this problem, the final price (Shyam's cost price) is Rs. 1430, the first profit is 20%, and the second profit is 40%. The original cost price is Ram's cost price \(C_R\).
\(1430 = C_R \times \left(1 + \frac{20}{100}\right) \times \left(1 + \frac{40}{100}\right)\)
\(1430 = C_R \times (1.20) \times (1.40)\)
\(1430 = C_R \times 1.68\)
\(C_R = \frac{1430}{1.68}\)
This confirms our step-by-step calculation and provides a general formula for handling successive profits.
Similar Questions
A shopkeeper uses 940 gm weight in place of one kg weight. He sells it at 4% profit. What will be the actual profit percentage? (rounded off to two decimal places)
A shopkeeper purchases six small cold drink bottles for ₹100. For how much should he sell one such bottle to get a profit of 20%?
A sold an article to B at 25% profit and B further sold it to C by earning a certain profit. If the cost price of C is 30% more than the cost price of A, then find the profit percentage earned by B.
If successive discounts of 5%, 10% and p% are equivalent to a single discount of 31.6%, then the value of p is:
Successive discounts of 10% and 10% are equivalent to a single discount of:
Two successive discounts of 20% and 25% on the marked price of an article are equal to a single discount of Rs. 250. If the marked price of the article is 25% above the cost price, the cost price (in Rs.) of the article is:
A household appliances company offers two successive discounts of 20% and 35% on the sale of a food processor. What is the final sale price (in Rs, to the nearest rupee) of a food processor costing Rs. 4580?
Some fruits are bought at 15 for Rs. 140 and an equal number of fruits at 10 for Rs. 120. If all the fruits are sold at Rs. 132 per dozen, then what is the profit percent in the entire transaction?
On selling an article for Rs. 246.80, the gain is 20% more than the amount of loss incurred on selling it for Rs. 216. If the article is sold for Rs. 220.75, then what is the gain/loss percent (correct to nearest integer)?
Radha purchased a Computer table for Rs. 10000 and a Centre table for Rs. 5000. She sold Computer table with 8% profit. With what profit percent should she sell the Centre table so as to gain 10% on the whole transaction.
Important Questions from Successive Selling
Rohan purchased a table at the rate of Rs. 275 per table. If he sells 16 tables for Rs. 5060, then what will be the profit percentage?
the cost price of an article is 30% less than the selling price of that article, then what will be the profit percentage?
A single discount equivalent to three successive discounts i.e. 7%, 12% and 5% is:
Two successive discounts, with the first being 10%, were given on an article having the marked price of ₹ 7,500. Finally, it was sold for ₹ 5,805. What percent was the second discount ?
The marked price of an article is ₹450. It is sold for ₹267.30, after offering three successive discounts of 10%, x%, and 20%. What is the value of x?
