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

Chapter 13 Profit Loss Discount And Value Added Tax – Exercise 13.2 | Set 1

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