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A man sells an article at a profit of 25%. If he had bought it at 20% less and soldit for Rs 36.75 less, he would have gained 30%. Find the cost price of the article.

Answer:

Let us consider the cost price of article be Rs x

The Profit percent is = 25% of 100 = 25/100

Selling price of article = x + x × 25/100

= x + x/4

= (4x+x)/4

= Rs 5x/4

If cost price of article is 20% less (given) = 20% of 100 = 20/100

Now, cost price is = x - x×20/100

= x – x/5

= (5x-x)/5

= Rs 4x/5

Now, selling price is = Rs5x/4 – 36.75

The Profit percent is = 30% of 100 = 30/100

He would have gained 30% selling at that price (Given)

We know that,

Gain = SP – CP

= 5x/4 – 36.75 – 4x/5

= (25x – 16x)/20 – 36.75

= 9x/20 – 36.75

Gain % = (gain/cost price) × 100

30% = [{(5x/4) – 36.75} - (4x/5)] / (4x/5) × 100

30/100 = (9x/20 – 36.75) / (4x/5) × 100 x = 175

∴ Cost price of article is Rs 175

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