By selling an article at ₹270 a man losses 10%. At what price should he sell it so as to get 20%?

Questions : By selling an article at ₹270 a man losses 10%. At what price should he sell it so as to get 20%?

Answer:  

 Let the cost price (CP) of the article be ₹x.

Since he loses 10% when selling at ₹270, we can write:

$$\text{Selling Price (SP)} = 90\% \text{ of } \text{Cost Price (CP)}$$ $$270 = \frac{90}{100} \times x$$ $$x = \frac{270 \times 100}{90} = 300$$

So, the cost price of the article is ₹300.

Now, to get a 20% profit, the new selling price should be:

$$\text{New SP} = 120\% \text{ of } \text{CP}$$ $$= \frac{120}{100} \times 300$$ $$= 360$$

So, the article should be sold at ₹360 to gain 20% profit.

Additional Techniques 

Here's how to solve this problem:

1. Find the cost price:

   • If selling at ₹270 results in a 10% loss, then ₹270 represents 90% of the cost price.
   • Let the cost price be 'C'.
   • 0.90 * C = ₹270
   • C = ₹270 / 0.90
   • C = ₹300

2. Calculate the selling price for a 20% profit:

   • To gain a 20% profit, the selling price should be 120% of the cost price.
   • Selling Price = 1.20 * C
   • Selling Price = 1.20 * ₹300
   • Selling Price = ₹360

Therefore, the man should sell the article for ₹360 to get a 20% profit.

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