 Hello and welcome to the session. In this session we will discuss the following question and the question says an article was sold at a loss of 5% had it been sold for $30 more there would have been a profit of 10% find the cost price. Let's start the solution now we have to find the cost price of the article first we will do an assumption let the cost price be $100 we are given that loss is 5% so loss is equal to 5% of cost price which is $100 and this is equal to 5 upon 100 into $100 zeros get cancelled and this is equal to $5 therefore selling price in the first case is equal to the cost price which is $100 minus loss which is $5 and this is equal to $95 also it is given that had it been sold for $30 more there would have been a profit of 10% so in the second case of it is equal to 10% of the cost price which is $100 this is equal to 10 upon 100 into $100 the zeros get cancelled and this is equal to $10 so therefore selling price in the second case is equal to the cost price which is $100 plus the profit which is $10 this is equal to $110 now the difference between two selling prices is equal to $110 minus $95 and this is equal to $15 we had assumed the cost price to be $100 so when the difference in selling prices is $15 cost price is equal to $100 in the question we are given that the difference in the selling prices is $30 and we have to find the cost price so therefore when the difference in selling prices is $30 cost price is equal to $100 upon $15 into $30 now $15 two times is $30 so this is equal to $200 the cost price is equal to $200 and this is the final answer with this we end our session hope you enjoyed the session