A retailer marks his price 10% above cost, another retailer arranges his price so that he will have a profit of 20% on his returns. If the
manufacture's price for an article is Rs. 50, what is the difference
between the retailers selling prices? What percent discount should the
retailer with higher price give, so that the profit would be equal?

The answer is below

Step-by-step explanation:

The cost price (manufacturing price) of an article is Rs.50.

Retailer 1 marks his price 10% above cost, hence the selling price for retailer 1 is:

Selling price for retailer 1 = 10% of Rs.50 + Rs.50 = (0.1 * Rs.50) + Rs.50 = Rs.55

Retailer 2 sets a profit of 20% on his returns, hence the selling price for retailer 2 is:

Selling price for retailer 2 = 20% of Rs.50 + Rs.50 = (0.2 * Rs.50) + Rs.50 = Rs.60

The difference  between the retailers selling prices = Rs.60 - Rs.50 = Rs.10

The retailer with the highest price sells for Rs.60 and the difference between the retailers selling prices is Rs.10. For the profit to be equal, the percentage discount is:

Discount = (Rs.10 / Rs.60) * 100% = 16.67%

use distributive property on all like terms and change your signs if you have a double negative or if you have positive/negative