## Chapter 9 – Discount and Commission

**Practice set 9.1**

**1. If marked price = ₹ 1700, selling price = ₹ 1540 then find the discount. **

**1. If marked price = ₹ 1700, selling price = ₹ 1540 then find the discount.**

**Solution:**

**Marked price = Rs 1700,**

**Selling price = Rs 1540**

**We know that,**

**Selling price = Marked price – Discount**

**∴ 1540 = 1700 – Discount**

**∴ Discount = 1700 – 1540**

**∴ Discount = Rs 160**

**Ans:** The amount of discount is Rs 160.

**2. If marked price = ₹ 990 and percentage of discount is 10, then find the selling price.**

**2. If marked price = ₹ 990 and percentage of discount is 10, then find the selling price.**

**Solution:**

**Marked price = Rs 990,**

**Discount = 10%**

**Let the percentage of discount be x**

**∴ x = 10%**

**We know that,**

**Discount = \(\large \frac {Marked\, Price\,×\,x}{100}\)**

**∴ Discount = \(\large \frac {990\,×\,10}{100}\)**

**∴ Discount = \(\large \frac {9900}{100}\)**

**∴ Discount = ₹ 99**

**Now,**

**Selling price = Marked price – Discount**

**∴ Selling price = 990 – 99**

**∴ Selling price = Rs 891**

**Ans:** The selling price is Rs 891.

**3. If selling price = ₹ 900. Discount is 20%, then find the marked price.**

**3. If selling price = ₹ 900. Discount is 20%, then find the marked price.**

**Solution:**

**Selling price = Rs 900**

**Discount = 20%**

**Let the marked price be Rs 100**

**Since, the discount given = 20%**

**∴ Amount of discount = Rs 20**

**We know that,**

**Selling price = Marked price – Discount**

**∴ Selling price = 100 – 20**

**∴ Selling price = Rs 80**

**Let actual marked price be Rs x**

**∴ For marked price of Rs x, selling price is Rs 900**

**\(\large \frac {80}{100}\) = \(\large \frac {900}{x}\)**

**∴ 80 × x = 100 × 900**

**∴ x = \(\large \frac {100\,×\,900}{2}\)**

**∴ x = Rs 1125**

**Ans:** The marked price is Rs 1125.

**4. The marked price of the fan is 3000 rupees. Shopkeeper gave 12% discount on it. Find the total discount and selling price of the fan. **

**4. The marked price of the fan is 3000 rupees. Shopkeeper gave 12% discount on it. Find the total discount and selling price of the fan.**

**Solution:**

**Marked price = Rs 3000**

**Discount = 12%**

**Let the percentage of discount be x.**

**∴ x = 12%**

**We know that,**

**Discount = \(\large \frac {Marked\, Price\,×\,x}{100}\)**

**∴ Discount = \(\large \frac {3000\,×\,12}{100}\)**

**∴ Discount = \(\large \frac {36000}{100}\)**

**∴ Discount = ₹ 360**

**Now,**

**Selling price = Marked price – Discount**

**∴ Selling price = 3000 – 360**

**∴ Selling price = Rs 2640**

**Ans:** The selling price is Rs 2640.

**5. The marked price of a mixer is 2300 rupees. A customer purchased it for Rs.1955. Find percentage of discount offered to the customer. **

**5. The marked price of a mixer is 2300 rupees. A customer purchased it for Rs.1955. Find percentage of discount offered to the customer.**

**Solution:**

**Marked price = Rs 2300,**

**Selling price = Rs 1955**

**We know that,**

**Selling price = Marked price – Discount**

**∴ 1955 = 2300 – Discount**

**∴ Discount = 2300 – 1955**

**∴ Discount = Rs 345**

**Let the percentage of discount be x**

**\(\large \frac {x}{100}\) = \(\large \frac {Discount}{Marked\,Price}\)**

**∴ \(\large \frac {x}{100}\) = \(\large \frac {345}{2300}\)**

**∴ x = \(\large \frac {345}{2300}\) × 100**

**∴ x = \(\large \frac {345}{23}\)**

**∴ x = 15%**

**Ans:** The percentage of discount offered to the customer is 15%.

**6. A shopkeeper gives 11% discount on a television set, hence the cost price of it is Rs. 22,250. Then find the marked price of the television set.**

**6. A shopkeeper gives 11% discount on a television set, hence the cost price of it is Rs. 22,250. Then find the marked price of the television set.**

**Solution:**

**Selling price = Rs 22,250**

**Discount = 11%**

**Let marked price be Rs 100**

**Since, the discount given = 11%**

**∴ Amount of discount = Rs 11**

**We know that,**

**Selling price = Marked price – Discount**

**∴ Selling price = 100 – 11 **

**∴ Selling price = Rs 89**

**Let actual marked price be Rs x**

**∴ For marked price of Rs x, selling price is Rs 22,250**

**\(\large \frac {89}{100}\) = \(\large \frac {22250}{x}\)**

**∴ x × 89 = 100 × 22250**

**∴ x = \(\large \frac {22250}{89}\) × 100**

**∴ x = 250 × 100**

**∴ x = Rs 25,000**

**Ans:** The marked price of the television set is Rs 25,000.

**7. After offering discount of 10% on marked price, a customer gets total discount of 17 rupees. To find the cost price for the customer, fill in the following boxes with appropriate numbers and complete the activity. **

**7. After offering discount of 10% on marked price, a customer gets total discount of 17 rupees. To find the cost price for the customer, fill in the following boxes with appropriate numbers and complete the activity.**

**Suppose, marked price of the item = 100 rupees**

**Therefore, for customer that item costs ___ – ___ = 90 rupees**

**Hence, when the discount is ___ then the selling price is ___ rupees.**

**Suppose when the discount is ___ rupees, the selling price is x rupees.**

**∴ \(\large \frac {x}{□}\) = \(\large \frac {□}{□}\)**

**∴ x = \(\large \frac {□\,×\,□}{□}\)**

**∴ x = \(\large □\)**

**∴ The customer will get the item for 153 rupees. **

** **

**Solution:**

**Suppose, marked price of the item = 100 rupees**

**Therefore, for customer that item costs 100 – 10 = 90 rupees**

**Hence, when the discount is 10 then the selling price is 90 rupees.**

**Suppose when the discount is 17 rupees, the selling price is x rupees.**

**∴ \(\large \frac {x}{17}\) = \(\large \frac {90}{10}\)**

**∴ x = \(\large \frac {90\,×\,17}{10}\)**

**∴ x = 153**

**∴ The customer will get the item for 153 rupees. **

**8. A shopkeeper decides to sell a certain item at a certain price. He tags the price on the item by increasing the decided price by 25%. While selling the item, he offers 20% discount. Find how many more or less percent he gets on the decided price.**

**8. A shopkeeper decides to sell a certain item at a certain price. He tags the price on the item by increasing the decided price by 25%. While selling the item, he offers 20% discount. Find how many more or less percent he gets on the decided price.**

**Solution:**

**Increase in the Price = 25%,**

**Discount offered = 20%**

**Let the decided price be Rs 100**

**∴ Increase in price = Rs 25**

**∴ Shopkeeper marks the price = 100 + 25 = Rs 125**

**∴ Marked price = Rs 125**

**Let the percentage of discount be x**

**∴ x = 20%**

**We know that,**

**Discount = \(\large \frac {Marked\, Price\,×\,x}{100}\)**

**∴ Discount = \(\large \frac {125\,×\,20}{100}\)**

**∴ Discount = \(\large \frac {2500}{100}\)**

**∴ Discount = ₹ 25**

**Now,**

**Selling price = Marked price – Discount**

**∴ Selling price = 125 – 25**

**∴ Selling price = Rs 100**

**∴ If the decided price is Rs 100, then shopkeeper gets Rs 100.**

**Hence, the shopkeeper gets neither more nor less than the decided price i.e. he gets 0% more or less on the decided price.**

**Practice set 9.2**

**Practice set 9.2**

**1. John sold books worth rupees 4500 for a publisher. For this he received 15 % commission. Complete the following activity to find the total commission John obtained.**

**1. John sold books worth rupees 4500 for a publisher. For this he received 15 % commission. Complete the following activity to find the total commission John obtained.****Selling price of books = ___**

**Rate of commission = ___**

** **

**Commission obtained = \(\large \frac {□\,×\,□}{□}\)**

** **

**∴ Commission = ___ rupees**

** **

**Solution:**

**Selling price of books = 15%**

**Rate of commission = 15% of Selling Price**

** **

**Commission obtained = \(\large \frac {15\,×\,4500}{100}\)**

** **

**∴ Commission = 675 rupees**

**2. Rafique sold flowers worth ₹ 15,000 by giving 4% commission to the agent. Find the commission he paid. Find the amount received by Rafique.**

**2. Rafique sold flowers worth ₹ 15,000 by giving 4% commission to the agent. Find the commission he paid. Find the amount received by Rafique.****Solution:**

**Selling price of flowers = Rs 15,000,**

**Rate of commission = 4%**

** **

**Commission = 4% of selling price**

**∴ Commission = \(\large \frac {4}{100}\) × 15,000**

**∴ Commission = 4 × 150**

**∴ Commission = Rs 600**

** **

**Now,**

**Amount received by Rafique = Selling Price – Commission **

**∴ Amount received by Rafique = 15,000 – 600**

**∴ Amount received by Rafique = Rs 14,400**

** **

**Ans:** Rafique paid Rs 600 as commission and the amount received by him was Rs 14,400.

**3. A farmer sold foodgrains for 9200 rupees through an agent. The rate of commission was 2%. How much amount did the agent get?**

**3. A farmer sold foodgrains for 9200 rupees through an agent. The rate of commission was 2%. How much amount did the agent get?****Solution:**

**Selling price of food grains = Rs 9200**

**Rate of commission = 2%**

**∴ Commission = 2% of selling price**

**∴ Commission = \(\large \frac {2}{100}\) × 9200**

**∴ Commission = 2 × 92**

**∴ Commission = Rs 184**

**Ans:** The agent got a commission of Rs 184.

**4. Umatai purchased the following items from a Khadi – Bhandar.**

**(i) 3 sarees for 560 rupees each.**

**(ii) 6 bottles of honey for 90 rupees each.**

**On the purchase, she received a rebate of 12%. How much total amount did Umatai pay ?**

**On the purchase, she received a rebate of 12%. How much total amount did Umatai pay ?****Solution: **

**Number of sarees = 3**

**Price of each saree = Rs 560**

**∴ Cost of 3 sarees **

**= 560 × 3**

**= Rs 1680 …(i)**

** **

**Number of honey bottles = 6,**

**Price of each bottle = Rs 90**

**∴ Cost of 6 honey bottles **

**= 90 × 6**

**= Rs 540**

** **

**Total amount of purchase**

**= Cost of 3 sarees + Cost of 6 honey bottles**

**= 1680 + 540**

**= Rs 2220**

** **

**Rate of rebate = 12%**

** **

**Rebate = 12% of total amount of purchase**

**∴ Rebate = \(\large \frac {12}{100}\) × 2220**

**∴ Rebate = 0.12 × 2220**

**∴ Rebate = Rs 266.40**

** **

**Amount paid by Umatai = Total amount of purchase – Rebate**

**∴ Amount paid by Umatai = 2,220 – 266.40 **

**∴ Amount paid by Umatai = Rs 1953.60**

** **

**Ans:** The total amount paid by Umatai is Rs 1953.60.

**5. Use the given information and fill in the boxes with suitable numbers.**

**5. Use the given information and fill in the boxes with suitable numbers.****Smt. Deepanjali purchased a house for ₹ 7,50,000 from Smt. Leelaben through**

**an agent. Agent has charged 2 % brokerage from both of them.**

**(1) Smt. Deepanjali paid \(\large □\) × \(\large \frac {□}{□}\)**

** = ₹ ___ brokerage for purchasing **

**the house.**

**(2) Smt. Leelaben paid brokerage of ₹ ___.**

**(3) Total brokerage received by the agent is ₹ ___.**

**(4) The cost of house Smt. Deepanjali paid is ₹ ___.**

**(5) The selling price of house for Smt. Leelaben is ₹ ___.**

**Solution: **

**Solution:****(1) Smt. Deepanjali paid 750000 × \(\large \frac {2}{100}\)**

** = ₹ 15000 brokerage for purchasing **

**the house.**

**(2) Smt. Leelaben paid brokerage of ₹ 15000.**

**(3) Total brokerage received by the agent is ₹ 15000 + 15000 = ₹ 30000.**

**(4) The cost of house Smt. Deepanjali paid is ₹ 7,50,000 + 15,000 = ₹ 7,65,000.**

**(5) The selling price of house for Smt. Leelaben is ₹ 7,50,000 – 15,000 = Rs 7,35,000.**