Std 8 Mathematics · Chapter 9

9. Discount and Commission

Solutions to Practice Sets 9.1 and 9.2 — discount, commission, brokerage and rebate, with every step shown. Maharashtra State Board (Balbharati), Standard Eight Mathematics.

Practice Set 9.1

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

Discount = Marked price − Selling price
= 1700 − 1540 = 160

Answer: Discount = ₹ 160

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

Discount = 990 × 10100 = ₹ 99
Selling price = Marked price − Discount = 990 − 99 = 891

Answer: Selling price = ₹ 891

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

If the marked price is ₹ 100, the discount is ₹ 20, so the selling price is 100 − 20 = ₹ 80.
Let the marked price be ₹ x when the selling price is ₹ 900.
∴ 80100 = 900x
∴ x = 900 × 10080 = 1125

Answer: Marked price = ₹ 1125

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

Discount = 3000 × 12100 = 30 × 12 = ₹ 360
Selling price = 3000 − 360 = 2640

Answer: Discount = ₹ 360, selling price = ₹ 2640

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

Discount = 2300 − 1955 = ₹ 345
Let the discount be x%. Then x100 = DiscountMarked price = 3452300
∴ x = 345 × 1002300 = 34523 = 15

Answer: 15% discount

6A shopkeeper gives 11% discount on a television set, hence its cost price (for the customer) is 22,250 rupees. Find the marked price of the television set.

If the marked price is ₹ 100, the customer pays 100 − 11 = ₹ 89.
Let the marked price be ₹ x when the customer pays ₹ 22,250.
∴ 89100 = 22250x
∴ x = 22250 × 10089 = 250 × 100 = 25,000

Answer: Marked price = ₹ 25,000

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

Suppose the marked price of the item = 100 rupees.
Therefore, for the customer that item costs 100 − 10 = 90 rupees.
Hence, when the discount is 10 rupees, the selling price is 90 rupees.
Suppose when the discount is 17 rupees, the selling price is x rupees.
∴ x90 = 1710 ∴ x = 17 × 9010 = 153

Answer: The customer will get the item for 153 rupees.

Check: the discount is 10% of the marked price, so the marked price is 170 rupees and 170 − 17 = 153.

8A 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.

Let the decided price be ₹ 100.
The price is tagged 25% more: marked price = 100 + 25 = ₹ 125.
Discount = 20% of 125 = 125 × 20100 = ₹ 25
Selling price = 125 − 25 = ₹ 100

So when the decided price is ₹ 100, he gets exactly ₹ 100. He gets neither more nor less.

Answer: 0% — he gets exactly the decided price.

A 25% increase followed by a 20% decrease does not give a 5% gain, because the 20% is taken on the bigger amount (₹ 125), not on ₹ 100.

Practice Set 9.2

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

Selling price of books = ₹ 4500 Rate of commission = 15%
Commission obtained = 4500 × 15100 ∴ Commission = 675 rupees

Answer: John obtained ₹ 675 commission.

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

Commission = 15000 × 4100 = 150 × 4 = ₹ 600
Amount received = 15000 − 600 = 14,400

Answer: Commission = ₹ 600; Rafique received ₹ 14,400

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

Commission = 9200 × 2100 = 92 × 2 = ₹ 184

Answer: The agent got ₹ 184.

4Umatai 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?

Cost of 3 sarees = 3 × 560 = ₹ 1680
Cost of 6 bottles of honey = 6 × 90 = ₹ 540
Total cost = 1680 + 540 = ₹ 2220
Rebate = 2220 × 12100 = 26640100 = ₹ 266.40
Amount to pay = 2220 − 266.40 = 1953.60

Answer: Umatai paid ₹ 1953.60

5Use 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. The agent charged 2% brokerage from both of them.

Brokerage from each person = 2% of 7,50,000

(1) Smt. Deepanjali paid 7,50,000 × 2100 = ₹ 15,000 brokerage for purchasing the house.
(2) Smt. Leelaben paid brokerage of ₹ 15,000.
(3) Total brokerage received by the agent is ₹ 30,000. (15,000 + 15,000)
(4) The cost of the house Smt. Deepanjali paid is ₹ 7,65,000. (price + her brokerage: 7,50,000 + 15,000)
(5) The selling price of the house for Smt. Leelaben is ₹ 7,35,000. (price − her brokerage: 7,50,000 − 15,000)

The buyer pays brokerage on top of the price, so her total cost goes up. The seller pays brokerage out of the price she receives, so the amount she actually gets goes down.

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