Question

A shopkeeper sells an item at a profit of 20%. If he had bought it at 10% less and sold it for 60 more, his profit would become 60%. What is the cost price of the item?

• A. 200
• B. 250
• C. 300
• D. 280

Hint:

When your algebraic solution doesn't match any of the given options, double-check your work. If it's still inconsistent, consider the possibility of a typo in the question's numbers and test if a small change (like 40% to 60%) makes one of the options work.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
This is a word problem involving profit and loss percentages under two different scenarios. We need to set up equations based on the given information to find the original cost price (CP).
Step 2: Key Formula or Approach:
The basic formulas for profit and loss are:
- \(\text{Selling Price (SP)} = \text{Cost Price (CP)} \times (1 + \frac{\text{Profit %}}{100})\)
- \(\text{Profit %} = \frac{\text{SP} - \text{CP}}{\text{CP}} \times 100\)
We will define the original cost price as a variable \(x\) and express the two scenarios algebraically.
Step 3: Detailed Explanation:
Let the original Cost Price (CP) be \(x\).
\[ 60 = \frac{(1.2x + 60) - 0.9x}{0.9x} \times 100 \] \[ 0.6 = \frac{0.3x + 60}{0.9x} \] \[ 0.6 \times (0.9x) = 0.3x + 60 \] \[ 0.54x = 0.3x + 60 \] \[ 0.54x - 0.3x = 60 \] \[ 0.24x = 60 \] \[ x = \frac{60}{0.24} = \frac{6000}{24} = 250 \] This value matches option (B).
Step 4: Final Answer
The original cost price of the item is 250.