Maharashtra Board Class 8 Maths Chapter 9 Discount and Commission Set 9.1 Solutions

Question 1. If marked price = Rs 1700, selling price = Rs 1540, then find the discount.
Answer: Solution:
Here, Marked price = Rs 1700,
selling price = Rs 1540
Selling price = Marked price - Discount
.:. 1540 = 1700 - Discount
.:. Discount = 1700 - 1540
= Rs 160
.:. The amount of discount is Rs 160.
In simple words: Discount is calculated as the difference between the marked price and the selling price. In this case, subtracting the selling price from the marked price directly gives the discount amount.

🎯 Exam Tip: Remember the basic formula: Discount = Marked Price - Selling Price. This is a fundamental concept for profit and loss calculations.

Question 2. If marked price Rs 990 and percentage of discount is 10, then find the selling price.
Answer: Solution:
Here, marked price = Rs 990,
discount = 10%
Let the percentage of discount be x
.:. x = 10%
i. Discount
\( = \frac{\text{Marked price} \times x}{100} \)
\( = \frac{990 \times 10}{100} \)
= Rs 99
ii. Selling price = Marked price - Discount
= 990 - 99
= Rs 891
.:. The selling price is Rs 891.
In simple words: First, calculate the amount of discount by finding 10% of the marked price. Then, subtract this discount amount from the marked price to get the final selling price.

🎯 Exam Tip: Always calculate the actual discount amount before determining the selling price when a percentage discount is given.

Question 3. If selling price Rs 900, discount is 20%, then find the marked price.
Answer: Solution:
Here, selling price = Rs 900, discount = 20%
Let the marked price be Rs 100
Since, the discount given = 20%
.:. Amount of discount = Rs 20
.:. Selling price = 100 - 20 = Rs 80
Let actual marked price be Rs x
.:. For marked price of Rs x, selling price is Rs 900
\( \frac{80}{100} = \frac{900}{x} \)
.:. 80 x x = 100 × 900
\( x = \frac{100 \times 900}{80} \)
.:. x = Rs 1125
.:. The marked price is Rs 1125.
In simple words: If a 20% discount means the selling price is 80% of the marked price, then you can use a proportion to find the original marked price when the selling price is known.

🎯 Exam Tip: When working backward from selling price and discount percentage to find the marked price, assume a base marked price (e.g., Rs 100) to set up a ratio or proportion.

Question 4. The marked price of the fan is Rs 3000. Shopkeeper gave 12% discount on it. Find the total discount and selling price of the fan.
Answer: Solution:
Here, Marked price = Rs 3000, discount = 12%
Let the percentage of discount be x.
.:. x = 12%
i. Discount
\( = \frac{\text{Marked price} \times x}{100} \)
\( = \frac{3000 \times 12}{100} \)
= 30 × 12
= Rs 360
ii. Selling price = Marked price - Discount
= 3000 - 360
= Rs 2640
.:. The total discount is Rs 360 and the selling price of the fan is Rs 2640.
In simple words: Calculate the 12% discount on the marked price of Rs 3000 to find the discount amount. Then, subtract this discount from the marked price to find the final selling price.

🎯 Exam Tip: This question requires two calculations: first, the discount amount, and second, the selling price. Ensure both are clearly presented for full marks.

Question 5. The marked price of a mixer is Rs 2300. A customer purchased it for Rs 1955. Find percentage of discount offered to the customer.
Answer: Solution:
Here, marked price = Rs 2300,
selling price = Rs 1955
i. Selling price = Marked price - Discount
.:. 1955 = 2300 - Discount
.:. Discount = 2300 - 1955
= Rs 345
ii. Let the percentage of discount be x
\( \frac{x}{100} = \frac{\text{Discount}}{\text{Marked price}} \)
\( \frac{x}{100} = \frac{345}{2300} \)
\( \text{.: } x = \frac{345}{2300} \times 100 \)
\( = \frac{345}{23} \)
.:. x = 15%
.:. The percentage of discount offered to the customer is 15%.
In simple words: First, find the discount amount by subtracting the selling price from the marked price. Then, express this discount as a percentage of the original marked price.

🎯 Exam Tip: Percentage discount is always calculated on the Marked Price. Use the formula: \(\frac{\text{Discount}}{\text{Marked Price}} \times 100\%\).

Question 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.
Answer: Solution:
Here, selling price = Rs 22,250, discount = 11%
Let marked price be Rs 100
Since, the discount given = 11%
.:. Amount of discount = Rs 11
.:. Selling price = 100 - 11 = Rs 89
.:. Let actual marked price be Rs x
.:. For marked price of Rs x, selling price is Rs 22,250
\( \frac{89}{100} = \frac{22,250}{x} \)
.:. x × 89 = 100 × 22,250
\( \text{.: } x = \frac{100 \times 22,250}{89} \)
= 100 × 250
.:. x = Rs 25,000
.:. The marked price of the television set is Rs 25,000.
In simple words: Since an 11% discount means the selling price is 89% of the marked price, you can use a proportion to find the original marked price given the selling price.

🎯 Exam Tip: When the selling price and discount percentage are known, and you need to find the marked price, consider what percentage of the marked price the selling price represents (100% - discount%).

Question 7. After offering discount of 10% on marked price, a customer gets total discount of Rs 17. To find the cost price for the customer, fill in the following boxes with appropriate numbers and complete the activity.
Answer: Solution:
Suppose, marked price of the item = Rs 100 Therefore, for customer that item costs 100 - 10 = Rs 90.
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.
\( \frac{x}{17} = \frac{90}{10} \)
\( \text{.: } x = \frac{90 \times 17}{10} \)
.:. x = 9 × 17
.:. x = 153
.:. The customer will get the item for Rs 153.
In simple words: By setting up a proportion based on the relationship between discount and selling price, you can find the customer's cost price for a different discount amount.

🎯 Exam Tip: For fill-in-the-blanks activities, ensure your calculations for the initial assumed values (e.g., marked price Rs 100) are correct as they form the basis for the proportion.

Question 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.
Answer: Solution:
Here, price increase = 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%
.:. Discount \( = \frac{\text{marked price} \times x}{100} \)
\( = \frac{125 \times 20}{100} \)
\( = \frac{2500}{100} \)
= Rs 25
.:. Selling price = Marked price - Discount
= 125 - 25
= Rs 100
.:. If the decided price is Rs 100, then shopkeeper gets Rs 100.
.:. The shopkeeper gets neither more nor less than the decided price i.e. he gets 0% more / less.
In simple words: Despite increasing the price by 25% and then offering a 20% discount, the final selling price turns out to be exactly the same as the original decided price, resulting in no net gain or loss percentage for the shopkeeper.

🎯 Exam Tip: When a price is first increased by a percentage and then discounted by another percentage, always calculate the new marked price first, and then apply the discount on that new marked price. Do not simply add and subtract percentages.

Maharashtra Board Class 8 Maths Chapter 9 Discount And Commission Practice Set 9.1 Intext Questions And Activities

Question 1. Write the appropriate numbers in the following boxes. (Textbook pg. no. 51)
Answer: Solution:
1. \( \frac{12}{100} \) = 12 percent = 12%
2. 47% = \( \frac{47}{100} \)
3. 86% = \( \frac{86}{100} \)
4. 4% of 300 = 300 × \( \frac{4}{100} \) = 12
5. 15% of 1700 = 1700 × \( \frac{15}{100} \) = 255
In simple words: This exercise reinforces the conversion between fractions, percentages, and calculating percentages of numbers. A percentage is simply a fraction out of 100.

🎯 Exam Tip: Practice converting between fractions and percentages regularly, as this forms the foundation for many percentage-based problems. Understanding that 'x% of a number' means \(\frac{x}{100} \times \text{number}\) is key.

Question 2. You may have seen advertisements like 'Monsoon Sale', 'Stock Clearance Sale' etc offering different discount. In such a sale, a discount is offered on various goods. Generally in the month of July, sales of clothes are declared. Find and discuss the purpose of such sales. (Textbook pg. no. 51)
Answer: Solution:
(Students should attempt the above activity on their own)
In simple words: Sales like 'Monsoon Sale' or 'Stock Clearance Sale' are often conducted by businesses to clear out old inventory, make space for new stock, attract more customers, and boost sales during specific periods.

🎯 Exam Tip: For descriptive questions or activities, focus on providing a clear and logical explanation. Think about the economic reasons behind sales and how they benefit both businesses and consumers.