Reena makes a profit of 20% by selling pens at a certain price. If she charges ₹5 more on each pen, she will gain 40%. The initial selling price of one pen was:
Solving for Initial Selling Price with Profit Percentages
This problem involves calculating the original selling price of an item (pens) given information about profit percentages at different selling prices. We need to determine the initial selling price when Reena makes a 20% profit, and how this changes when the price is increased.
Understanding the Key Information
Let's break down the information given:
- Initial scenario: Reena makes a 20% profit.
- Second scenario: If she increases the price by ₹5, she gains 40%.
- Goal: Find the initial selling price of one pen.
Calculations and Step-by-Step Solution
We can solve this using the concepts of Cost Price (CP) and Selling Price (SP). Let:
- CP = Cost Price of one pen
- SP1 = Initial Selling Price of one pen
- SP2 = New Selling Price after the increase
Step 1: Formulate equations based on the profit percentages.
When there is a profit percentage, the Selling Price (SP) is calculated as:
SP = CP * (1 + (Profit Percentage / 100))
From the first scenario (20% profit):
SP1 = CP * (1 + (20 / 100))
SP1 = CP * (1 + 0.20)
SP1 = 1.20 * CP (Equation 1)
From the second scenario (40% profit):
SP2 = CP * (1 + (40 / 100))
SP2 = CP * (1 + 0.40)
SP2 = 1.40 * CP (Equation 2)
Step 2: Relate the two selling prices.
We know that the new selling price (SP2) is ₹5 more than the initial selling price (SP1):
SP2 = SP1 + 5 (Equation 3)
Step 3: Solve the system of equations.
Substitute Equation 1 and Equation 2 into Equation 3:
(1.40 * CP) = (1.20 * CP) + 5
Now, rearrange the equation to solve for CP:
1.40 * CP - 1.20 * CP = 5
0.20 * CP = 5
CP = 5 / 0.20
CP = ₹25
Step 4: Calculate the initial selling price (SP1).
Using Equation 1:
SP1 = 1.20 * CP
SP1 = 1.20 * 25
SP1 = ₹30
Verification
Let's check if this matches the second scenario:
- Initial SP (SP1) = ₹30
- New SP (SP2) = SP1 + ₹5 = ₹30 + ₹5 = ₹35
- Cost Price (CP) = ₹25
- Profit in the second scenario = SP2 - CP = ₹35 - ₹25 = ₹10
- Profit Percentage = (Profit / CP) * 100 = (10 / 25) * 100 = 0.40 * 100 = 40%
This confirms our calculation. The initial selling price that yielded a 20% profit was ₹30.
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