Class 8 RD Sharma Solutions- Chapter 13 Profit Loss Discount And Value Added Tax - Exercise 13.2 | Set 2

Chapter 13 of RD Sharma's Class 8 textbook continues to explore commercial mathematics, with Exercise 13.2 | Set 2 focusing specifically on discount calculations. This set builds upon the concepts of profit and loss introduced earlier and introduces students to more complex scenarios involving discounts, marked prices, and selling prices. The exercise aims to enhance student's ability to calculate and analyze various discount situations, preparing them for real-world applications in consumer mathematics and basic business operations.

Question 14: A shopkeeper marks his goods in such a way that after allowing a discount of 25% on the marked price, he still makes a profit of 50%. Find the ratio of the C.P. to the M.P.

Solution:

Here, Discount% given to customer = 25%

       Profit% earned by shopkeeper = 50%

Using Formula, C.P = (S.P * 100)/(100 + Profit%)

Hence, C.P = (S.P * 100)/(100 + 50)

                 = (S.P * 100)/150

                 = (2 * S.P)/3

Using Formula, M.P = (S.P * 100)/(100 - Discount%)

Hence, M.P = (SP * 100)/(100 - 25)

               = (S.P * 100)/75

               = (4 * S.P)/3

Ratio of C.P to M.P = ((2 * S.P)/3)/ ((4 * S.P)/3)

                             = 1:2

Question 15: A cycle dealer offers a discount of 10% and still makes a profit of 26%. What is the actual cost to him of a cycle whose marked price is Rs 840?

Solution:

Here, M.P of the cycle = Rs 840

 Discount% given to customer = 10%

 Profit% earned by cycle dealer = 26%

To find C.P of cycle.

Using Formula, S.P = (M.P * (100 - Discount%))/100

Hence, S.P of goods = Rs (840 * (100 - 10))/100

                               = Rs (840 * 90)/100

                               = Rs 756

Using Formula, C.P = (S.P * 100)/(100 + Profit%)

Hence, C.P of goods = Rs (756 * 100)/(100 + 26)

                              = Rs (756 * 100)/126

                              = Rs 600

Question 16: A shopkeeper allows 23% commission on his advertised price and still makes a profit of 10%. If he gains Rs 56 on one item, find the advertised price.

Solution:

Here, Commission% = 23%       (It is same as discount percentage)

         Profit% of shopkeeper = 10%

         Profit of shopkeeper = Rs 56

Using Formula, Profit% = (Profit * 100)/C.P

Hence, C.P = (Profit * 100)/Profit%

Here C.P = Rs(56 * 100)/10

                = Rs 560

Using Formula, S.P = (C.P * (100 + Profit%))/100

Hence, S.P = Rs (560 * (100 + 10))/100

               = Rs (560 * 110)/100

               = Rs 616

Using Formula, M.P = (S.P * 100)/(100 - Discount%)              

Hence, M.P = Rs (616 * 100)/(100 - 23)

                 = Rs 800

Question 17: A shopkeeper marks his goods at 40% above the cost price but allows a discount of 5% for cash payment to his customers. What actual profit does he make, if he receives Rs 1064 after paying the discount?

Solution:

Here, Mark up percentage = 40%

        Discount% = 5%

       S.P of the goods = Rs 1064

Let the C.P of the goods be Rs y.

Then the M.P of the goods would be Rs 1.40y.

Using Formula, S.P = (M.P * (100 - Discount%))/100

Hence, S.P of the goods = Rs (1.40y  * (100 - 5))/100

                        Rs 1064 = Rs (1.40y * 95)/100

                    or y = Rs (1064 * 100)/(1.40 * 95)

                           = Rs106400/133

                           = Rs 800

Now Using Formula, Profit = (S.P - C.P)

           We have, Profit = Rs (1064 - 800)

                                      = Rs 264

Question 18: A publisher gives 32% discount on the printed price of a book to booksellers. What does a bookseller pay for a book whose printed price is Rs 275?

Solution:

Here, Discount% given by book publisher = 32%

          Printed price = Rs 275

Using Formula, S.P = (M.P * (100 - Discount%))/100

Hence, S.P of publisher or cost price of bookseller = Rs (275 * (100 - 32))/100

                                                                             = Rs (275 * 68)/100

                                                                             = Rs 187

Question 19: After allowing a discount of 20% on the marked price of a lamp, a trader loses 10%. By what percentage is the marked price above the cost price ?

Solution:

Here, Discount% on lamp = 20%

          Loss% on lamp = 10%

Let C.P be x.

Then S.P would be (9x)/10.

Using Formula, M.P = (S.P * 100)/(100 - Discount%)      

Hence, M.P = (((9x)/10) * 100))/(100 - 20)

                  = (9x * 10)/80

                  = (9x)/8

Mark up price = M.P - C.P

                         = (((9x) /8) - x)

                         = x/8

Mark up % = ((Mark up price * 100) / C.P)%

                   = ((x/8) * 100)/ x%

                    = 12.50%

Question 20: The list price of a table fan is Rs 480 and it and is available to a retailer at 25% discount. For how much should a retailer sell it to gain 15%?

Solution:

Here, List price of a table fan = Rs 480

        Discount% = 25%

       Profit% = 15%

To find S.P

C.P of retailer = (List price * (100 - Discount%))/100

                        = Rs (480 * (100 - 25))/100

                        = Rs (480 * 75)/100

                        = Rs 360

Using Formula, S.P = (C.P * (100 + Profit%))/100

Hence, S.P of the retailer = Rs (360 * (100 + 15))/100

                                         = Rs (360 * 115)/100

                                         = Rs 414

Question 21: A cycle merchant allows 20% discount on the marked price of the cycles and still makes a profit of 20%. If he gains Rs 360 over the sale of one cycle, find the marked price of the cycle. (in Rs.)

Solution:

Here, Discount% on cycle  = 20%

          Profit% on cycles = 20%

          Profit on cycles = Rs 360

Using Formula, Profit% = (Profit * 100)/C.P

Hence, C.P = (Profit * 100)/Profit%

Here C.P of cycles = Rs(360 * 100)/20

                            = Rs 1800

Using Formula, S.P = (C.P * (100 + Profit%))/100

Hence, S.P of cycles = Rs (1800 * (100 + 120))/100

               = Rs (1800 * 120)/100

               = Rs 2160

Using Formula, M.P of cycles = (S.P * 100)/(100 - Discount%)              

Hence, M.P = Rs (2160 * 100)/(100 - 20)

                = Rs 2700

Question 22: Jyoti and Meena run a ready-made garment shop. They mark the garments at such a price that even after allowing a discount of 12.5%, they make a profit of 10%. Find the marked price of a suit which costs them Rs 1470.

Solution:

Here, C.P of the garment = Rs 1470

        Discount% = 12.5%

       Profit% earned by Jyoti and Meera = 10%

To find M.P of the article.

Using Formula, S.P = (C.P*(100+Profit%))/100

Hence, S.P of the article = Rs (1470 * (100 + 10))/100

                                    = Rs (1470 * 110)/100

                                    = Rs 16170

Using Formula, M.P = (S.P * 100)/(100 - Discount%)

Hence, M.P of the article = Rs (16170 * 100)/(100 - 12.5)  

                                    = Rs (16170 * 100)/87.5

                                    = Rs 1848

Question 23: Jasmine allows 4% discount on the marked price of her goods and still earns a profit of  20%.  What is the cost price of a shirt for her marked at Rs 850?

Solution:

Here, M.P of the goods = Rs 850

Discount% given to customer = 4%

Profit% earned by jasmine = 20%

To find C.P of goods.

Using Formula, S.P = (M.P * (100 - Discount%))/100

Hence, S.P of goods = Rs (850 * (100 - 4))/100

                             = Rs (850 * 96)/100

                             = Rs 816

Using Formula, C.P = (S.P * 100)/(100 + Profit%)

Hence, C.P of goods = Rs (816 * 100)/(100 + 20)

                              = Rs (816 * 100)/120

                              = Rs 680

Question 24: A shopkeeper offers 10% off-season discount to the customers and still makes a profit of 26%. What is the cost price for the shopkeeper on a pair of shoes marked at Rs 1120?

Solution:

Here, M.P of the shoes = Rs 1120

Discount% given to customer =10%

Profit% earned by shopKeeper = 26%

To find C.P of shoes.

Using Formula, S.P = (M.P * (100 - Discount%))/100

Hence, S.P of goods = Rs (1120 * (100 - 10))/100

                             = Rs (1120 * 90)/100

                             = Rs 1008

Using Formula, C.P = (S.P * 100)/(100 + Profit%)

Hence, C.P of goods = Rs (1008 * 100)/(100 + 26)

                              = Rs (1008 * 100)/126

                              = Rs 800

Question 25: A lady shopkeeper allows her customers 10% discount on the marked price of the goods and still gets a profit of 25% what is the cost price of a fan for her marked at Rs 1250?

Solution:

Here, M.P of the fan = Rs 1250

Discount% given to customer =10%

Profit% earned by shopKeeper = 25%

To find C.P of shoes.

Using Formula, S.P = (M.P * (100 - Discount%))/100

Hence, S.P of fan = Rs (1250 * (100 - 10))/100

                             = Rs (1250 * 90)/100

                             = Rs 1125

Using Formula, C.P = (S.P * 100)/(100 + Profit%)

Hence, C.P of fan = Rs (1125 * 100)/(100 + 25)

                              = Rs (1125 * 100)/125)

                              = Rs 900

Summary

Exercise 13.2 | Set 2 of Chapter 13 delves deeper into discount calculations and their relationship with profit and loss. This set covers a wide range of scenarios, including simple discount calculations, problems involving marked prices and discounts, and more complex situations where discounts interact with profit percentages. The questions are designed to enhance students' analytical skills and their ability to navigate the often-confusing world of retail pricing. By working through these exercises, students learn to calculate selling prices after discounts, determine original prices from discounted prices, and analyze the impact of discounts on profit margins. This set helps students develop a more sophisticated understanding of commercial mathematics, bridging the gap between classroom learning and real-world financial literacy.