Math Problem Statement

A man bought 20 pens for Rs.x and the man sold each pen at the cost price of two pens. If he sold the pen at a loss of 20%, then he would have sold each pen for Rs.36 less. Find the total selling price of all pens, if he had sold each pen at a profit of 30%.

Solution

Let's break down the problem step by step.

Step 1: Define Variables

  • Let the cost price (CP) of each pen be yy Rs.
  • Therefore, the total cost price for 20 pens is 20y=x20y = x Rs.

Step 2: Understand Selling Price at a Loss

  • He sold each pen at the cost price of two pens, so the selling price (SP) of each pen is 2y2y Rs.
  • The loss is 20%, so the loss per pen is 0.20×y0.20 \times y Rs.
  • Hence, the selling price with a 20% loss would be y0.20y=0.80yy - 0.20y = 0.80y Rs.
  • According to the problem, this selling price is Rs.36 less than 2y2y.

Step 3: Formulate the Equation

  • The equation based on the above information is: 0.80y=2y360.80y = 2y - 36
  • Solving for yy: 0.80y=2y360.80y = 2y - 36 2y0.80y=362y - 0.80y = 36 1.20y=361.20y = 36 y=361.20=30 Rs.y = \frac{36}{1.20} = 30 \text{ Rs.}

Step 4: Find the Total Selling Price at 30% Profit

  • Now, if he sold each pen at a 30% profit, the selling price of each pen would be: [ \text{SP per pen} = y + 0

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Math Problem Analysis

Mathematical Concepts

Cost Price
Selling Price
Profit and Loss

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12