An article when sold at a discount of Rs. 100, the shopkeeper earns the profit of 140% and if it is sold at no discount, then profit will be 220%. Find the CP of the article.
Rs. 125
Understanding the Problem: Finding Article Cost Price
This problem involves calculating the Cost Price (CP) of an article based on two different selling scenarios involving profit and discount. We need to use the relationships between Cost Price, Selling Price (SP), Marked Price (MP), profit percentage, and discount amount.
Defining Variables and Formulas
- Let CP represent the Cost Price of the article.
- Let MP represent the Marked Price of the article.
- Let SP represent the Selling Price of the article.
- The formula relating SP, CP, and Profit Percentage is:
SP = CP + Profit
SP = CP * $\large(1 + \frac{\text{Profit Percentage}}{100}\large)$
- The formula relating SP, MP, and Discount is:
SP = MP - Discount
Analyzing Selling Scenario 1
In the first scenario, the article is sold at a discount of Rs. 100, and the shopkeeper earns a profit of 140%.
- Profit Percentage = 140%
- Discount = Rs. 100
- Using the profit formula:
SP$_1$ = CP * $\large(1 + \frac{140}{100}\large)$
SP$_1$ = CP * (1 + 1.40)
SP$_1$ = 2.40 * CP
- Using the discount formula:
SP$_1$ = MP - 100
- Equating the two expressions for SP$_1$:
2.40 * CP = MP - 100
- Rearranging to find an expression for MP:
MP = 2.40 * CP + 100 ...(Equation 1)
Analyzing Selling Scenario 2
In the second scenario, the article is sold with no discount, and the profit is 220%.
- Discount = 0
- Profit Percentage = 220%
- Using the profit formula:
SP$_2$ = CP * $\large(1 + \frac{220}{100}\large)$
SP$_2$ = CP * (1 + 2.20)
SP$_2$ = 3.20 * CP
- Since there is no discount, the Selling Price (SP$_2$) is equal to the Marked Price (MP):
MP = SP$_2$ = 3.20 * CP ...(Equation 2)
Calculating the Cost Price (CP)
Now we have two expressions for the Marked Price (MP). We can equate Equation 1 and Equation 2 to solve for CP.
- Equating the expressions for MP:
2.40 * CP + 100 = 3.20 * CP
- Subtract 2.40 * CP from both sides:
100 = 3.20 * CP - 2.40 * CP
100 = 0.80 * CP
- Solve for CP:
CP = $\large \frac{100}{0.80}$
CP = $\large \frac{100}{80/100}$
CP = $100 \times \large \frac{100}{80}$
CP = $100 \times \large \frac{10}{8}$
CP = $100 \times \large \frac{5}{4}$
CP = $\large \frac{500}{4}$
CP = 125
Therefore, the Cost Price (CP) of the article is Rs. 125.
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