Chapter 9 – Discount and Commission
Practice set 9.1
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.
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.
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.
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.
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.
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.
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.
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
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.
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?
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 ?
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.
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:
(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.