Question

a man sells an article at a gain of 10% If he had bought it for 10% less and sold it for rupees 10 he would have gained 25% find the cost price of the article

Answer 1

Hello there!
Let's start by assuming that the cost price of the article is Rs. X.

By the conditions given in the question, the man bought it for a 10% less price than the cost price.

So the man bought it at

$= x - \frac{10}{100} x \\ = \frac{90}{100} x \\ = \frac{9}{10} x$
Now if he sells the article at Rs 10, he would have a profit of 25%. This profit is calculated on the basis of the cost price.

So 100% is the cost price.
And (100+25)% of the cost price is the selling price, which is Rs 10.

Thus,

125% of (9/10)X = 10$\frac{125}{100} \times \frac{9}{10} \times x = 10 \\ 9x = 10 \times \frac{100 \times 10}{125} \\ 9x = 10 \times 8 \\ 9x = 80 \\ x = \frac{80}{9}$
Thus the original Cost Price is Rs 80/9 or Rs 8.8888...