 Hello and welcome to the session. In this session we are going to discuss the following question which says that a. Find single discount equivalent to the discount series 25%, 15%, 5% The list price of a radio is $120, a retailer pays $95.04, he gets successive discount of 10% and another rate which is illegible. What is the second discount rate? Now moving on to the solution, we need to find the single discount equivalent to the discount series 25%, 15% and 5%. Now let us suppose the selling price is $100. Now if we list 25% discount we get $100-$25 that is $75. Now $75 is the new selling price again less 15% discount on $75 that is 15% discount on $75 is 15 by 100 into 75 which gives 45 by 4 that is 11.25. Therefore we have $75-$11.25 which is equal to $63.75. Now our new selling price is $63.75. Now again if we list 5% discount on the new selling price that is $63.75 we get 5% of $63.75 that is 500 into 63.75 which is approximately equal to 3.19. So we have 63.75-$3.19 which is equal to $63.56. Therefore single discount equivalent to the discount series is given by minus $63.56 which is equal to $39.44. Therefore single discount is $39.45 on a list price of $100 is equal to 39.44%. Therefore the single discount equivalent to discount series 25%, 15%, 5%, 9.44% which is the required answer. Now the second part of the question says that the list price of a radio is given as $120 and the retailer pays $95.04. He gets successive discounts of 10% and another rate which is illegible and we need to find out the second discount rate. The list price of the radio is given as $120. First discount is given as 10%. Therefore discount will be equal to 10% of $120 which is equal to 10 upon 100 into 120 that is $12. Therefore the price after first discount is equal to $120-$12 which is equal to $108. Now we know that the retailer pays $95.04. Therefore discount on $108 is given by $108-$95.04 which is equal to $12.95. So discount on $108 is equal to $12.96. Therefore discount on $100 will be given by $12.96 upon 108 into $100 which is equal to $1,296 by $108 which is equal to $12. Again the discount rate is 12% which is the required answer. This completes our session. Hope you enjoyed this session.