Class 8 RD Sharma Solutions - Chapter 13 Profit Loss Discount And Value Added Tax - Exercise 13.3 | Set 1

In Class 8 Mathematics, Chapter 13 focuses on fundamental concepts of profit, loss, discount and value-added tax (VAT). These concepts are essential for the understanding real-world financial transactions and calculations. Exercise 13.3 | Set 1 helps students apply these concepts to solve practical problems involving the profit and loss, discounts and VAT.

Profit, Loss, Discount and Value Added Tax

Profit and Loss: These are basic financial terms used to calculate the gain or loss from the selling goods. The Profit is the amount earned when the selling price is higher than the cost price while loss occurs when the selling price is lower than the cost price.

Discount: A discount is a reduction applied to the original price of an item often expressed as a percentage. The Discounts are commonly used in the sales and marketing to the attract customers.

Value Added Tax (VAT): The VAT is a type of indirect tax imposed on the value added to the goods and services at each stage of the production or distribution. It is calculated as a percentage of the selling price and is an important aspect of the business transactions.

Question 1. The list price of a refrigerator is Rs.9700. If a value-added tax of 6% is to be charged on it, how much one has to pay to buy the refrigerator?

Solution:

List price of the refrigerator = Rs. 9700

VAT = 6%

So, VAT = 6% of Rs. 9700

             = 6/100 × 9700

             = Rs. 582

The total amount to be paid will be (Rs. 9700 + Rs. 582) = Rs. 10282

Hence, the total one has to pay to buy the refrigerator is Rs. 10282.

Question 2. Vikram bought a watch for Rs. 825. If this amount includes 10% VAT on the price list, what was the list price of the watch? 

Solution:

Let the list price of the watch be Rs. x

Vikram bought it for (Rs. x + 10x/100) = Rs. 825 

                                          ⇒ x + 0.1x = 825

                                         ⇒ 1.1x = 825 

                                         ⇒ x = 825 / 1.1 

                                        ⇒ x = 8250/11

                                       ⇒ x = 750

Thus, the price of Watch is Rs. 750

Question 3. Aman bought a shirt for Rs. 347.50 which includes 7% VAT. Find the list price of the shirt.

Let the price of shirt be Rs. x 

Then, 

Aman bought the shirt for (Rs. x + Rs. 7x/100) = Rs. 347.50

                                     ⇒ x + 7x/100 = 347.50 

                                    ⇒ 107x/100 = 347.50

                                    ⇒ x = (347.50 × 100) / 107

                                    ⇒ x = 350

Hence, the price of the shirt is Rs. 350

Question 4. Rani purchases a pair of shoes whose sale price is Rs. 175. If she pays VAT at the same rate of 7%, how much amount does she pay VAT? Also, find the net value of the pair of shoes.

Solution:

Given,  

Selling price of shoes = Rs. 175

VAT = 7 %

Therefore, 7% of 175

⇒ 7/100 × 175

⇒ Rs. 12.25

Rani has to pay Rs. 12.25 as VAT also, the net value of shoes ( VAT + Price) is Rs. 12.25 +  Rs. 175 = Rs. 187.25

Question 5. Swarna paid Rs. 20 as VAT on a pair of shoes worth Rs. 250. find the rate of the VAT.

Solution:

Given,  

Amount paid by Swarna for a pair of shoes = Rs. 250

VAT paid by her = Rs. 20

Let the rate of VAT be x % 

Then, x% of 250 = 20 

⇒ x/100 × 250 = 20 

⇒ x = (20 × 10) / 25

⇒ x = 8 

Hence, Swarna paid 8% VAT on her pair of shoes.

Question 6. Sarita buys goods worth Rs. 5500. She gets a rebate of 5% on it. After getting the rebate if VAT at the rate of 5% is charged, find the amount she will have to pay for the goods.

Price after getting a rebate of 5% on Rs. 5500

⇒ 5% on Rs. 5500

⇒ 5 /100 × 5500 

⇒ Rs. 275

So, the new cost = Rs. 5500 - Rs. 275 = Rs. 5225

Now, VAT = 5%

Then, 5% of Rs. 5225 

        ⇒ 5/100 × 5225

        ⇒ Rs. 261.25

The amount to be paid for the goods is Rs.5225 + Rs. 261.25 = Rs. 5486.25

Question 7. The cost of furniture inclusive of the VAT is Rs. 7150. if the rate of the VAT is Rs. 105, find the original cost of the furniture.

Cost of furniture inclusive of VAT = Rs. 7150 

Let the original cost be Rs. x

Cost of furniture ⇒ 10% of x + x = Rs. 7150

                          ⇒ 10/100 × x + x = 7150

                          ⇒ 0.1x + x = 7150

                          ⇒ 1.1x = 7150

                          ⇒ x = (7150 × 10)/11

                          ⇒ x = Rs. 6500

Thus, The original cost of furniture is Rs. 6500

Question 8. A furniture is available for Rs. 13750 including VAT. If the rate of the VAT is 10%, find the original cost of the furniture.

Given,

Cost of the furniture inclusive VAT is Rs. 13750

Let the original price of furniture be Rs. x 

Cost of furniture = 10% of Rs. x + Rs. x is Rs. 13750

                           ⇒ 10/100 × x + x = 13750

                          ⇒ 0.1x + x = 13750

                          ⇒ 1.1x = 13750

                          ⇒ x = (13750 × 10) / 11

                          ⇒ x = Rs. 12500

Hence, the original price of furniture is Rs. 12500.

Question 9.  A colour T.V is available for Rs. 13440 including VAT. If the original cost of T.V is Rs.12000. Find the rate of VAT.

Given,

The cost of T.V including VAT = Rs. 13440

Original cost of T.V = Rs. 12000

Let, the rate of VAT be x% 

Cost of the T.V is x% of Rs. 12000 + Rs. 12000 is Rs. 13440

                         ⇒ x/100 × 12000 + 12000 = 13440

                         ⇒ 120x + 12000 = 13440

                         ⇒ 120x = 13440 - 12000

                         ⇒ x = 1440 / 120

                         ⇒ x = 12 

The VAT rate on color T.V is 12%

Question 10. Reena goes to a shop to buy a radio, costing Rs. 2568. The rate of the VAT is 7%. She tells the shopkeeper to reduce the price of radio such that she has to pay Rs. 2568, inclusive VAT. Find the reduction needed at the price of the radio.

Let the reduced price, excluding the VAT , of the radio be Rs. x

Then VAT = 7% of Rs. x 

                ⇒ 0.07x

S.P of the radio= Rs. x + Rs. 0.07x

                         = 1.07x

S.P is given as Rs. 2568

                   ⇒ 1.07x = 2568

                   ⇒ x = (2568 × 100) / 107 

                   ⇒ x = Rs. 2400

So, the reduction in the price of radio is Rs. 2568 - Rs. 2400

                                                            = Rs. 168

The reduction needed at the price of radio is Rs. 168 

Chapter 13 Profit Loss Discount And Value Added Tax – Exercise 13.3 | Set 2

Conclusion

Understanding profit, loss, discount and VAT is crucial for the managing finances effectively and making informed purchasing decisions. Exercise 13.3 | Set 1 in RD Sharma's Chapter 13 provides the valuable practice in applying these concepts to solve the various mathematical problems. Mastery of these topics not only aids in academic success but also equips students with the practical skills for the everyday financial management.