 Hello and welcome to this session. In this session we will discuss the following question and the question says, Paul sold some 100 dollar shares at 15% discount and invested in 50 dollar shares at 25 dollars, carrying a dividend of 10%. Had he sold his shares at 20% premium instead of 15% discount, he would have earned 390 dollars more. Signed the number of shares sold by him. Let's start the solution now. Suppose Paul sells x shares, we are given that the price of each share is 100 dollars and Paul sells each share at 15% discount. So selling price of one share at 15% discount is equal to the price of each share that is 100 dollars minus 15 upon 100 into 100 dollars. Zeros get cancelled. So this is equal to 100 dollars minus 15 dollars which is equal to 85 dollars. So therefore selling price of x shares 15% discount is equal to 85 into x dollars which is equal to 85 x dollars. Now we will calculate the selling price of one share if he sold it at 20% premium. Instead of 15% discount, so the selling price of one share at 20% premium is equal to the price of one share that is 100 dollars plus 20 upon 100 into 100 dollars. Zeros get cancelled and this is equal to 100 dollars plus 20 dollars which is equal to 120 dollars. So therefore selling price of x shares 20% premium is equal to 120 into x dollars which is equal to 120 x dollars. It is given that he invested in 50 dollars shares at 25 dollars carrying a dividend of 10% that is the nominal value of the shares is 50 dollars and the market value is 25 dollars. So therefore number of shares whose nominal value is 50 dollars that can be purchased with 85 x dollars which is the selling price of x shares at 15% discount is equal to 85 x dollars upon the market value of each share which is given to be 25 dollars. So we write 25 dollars which is equal to 85 x upon 25. Now the dividend is 10%. So the income received or dividend received on these shares is equal to 10% of the nominal value into the total number of shares that is 10 upon 100 into the nominal value which is 50 into the number of shares which is 85 x upon 25 dollars. Zeros get cancelled and 5 5 times is 25 also 5 17 times is 85. So this is equal to 17 x dollars. Similarly number of shares whose nominal value is 50 dollars that can be purchased 120 x dollars which is the selling price of x shares at 20% premium is equal to 120 x dollars upon the market value of each share which is 25 dollars. This is equal to 120 x upon 25. Therefore dividend received on these shares is equal to 10% of the nominal value that is 10 upon 100 into 50 into total number of shares which is 120 x upon 25 dollars. Zeros get cancelled and 5 5 times is 25 also 5 24 times is 120. So this is equal to 24 x dollars we are given that had he sold his shares at 20% premium instead of 16% premium he would have earned 490 dollars more that is it is given that 24 x dollars which is the income received if he sold the shares at 20% premium minus 17 x dollars which is the income received if he sold the shares at 15% discount is equal to 490 dollars. This implies 7 x dollars is equal to 490 dollars this implies x is equal to 490 upon 7 and 7 70 times is 490. This implies x is equal to 70. So the final answer is the number of shares sold by all is equal to 70 with this we end our session hope you enjoyed the session.