A man sales an article at a loss of 10%, if he had sold the article at ₹30 more, he could have got a profit 5%, find his cost price

Questions : A man sales an article at a loss of 10%, if he had sold the article at ₹30 more, he could have got a profit 5%, find his cost price?

Answer:  

Shortcut Formula:

$$\text{Cost Price} = \frac{\text{Difference in Selling Price}}{\text{Profit \% + Loss \%}} \times 100$$

Applying the Formula:

• Given loss = 10%
• Given profit = 5%
• Difference in selling price = ₹30

Now, using the formula:

$$CP = \frac{30}{10 + 5} \times 100$$ $$CP = \frac{30}{15} \times 100$$ $$CP = 2 \times 100 = 200$$

Thus, the cost price is ₹200, calculated quickly using the shortcut!

Additional Techniques 

Here's how to solve this problem:

1. Understand the relationships:

   • Selling at a 10% loss means the selling price is 90% of the cost price.
   • Selling at a 5% profit means the selling price is 105% of the cost price.

2. Set up variables:

   • Let 'C' be the cost price.

3. Create equations:

   • Selling price at a 10% loss: 0.90C
   • Selling price at a 5% profit: 1.05C

4. Relate the two selling prices: The problem states that if the man had sold the article for ₹30 more, he would have made a 5% profit. This means the difference between the two selling prices is ₹30.

   1.05C - 0.90C = 30

5. Solve for the cost price (C):

   0.15C = 30

   C = 30 / 0.15

   C = 200

Answer: The man's cost price for the article was ₹200.

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