Chapter 13 - Proft, Loss, Discount and Value Added Tax (VAT) (Part -3), Class8 RD Sharma Solutions | RD Sharma Solutions for Class 8 Mathematics PDF Download

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Question 1:

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

ANSWER:

List price of the refrigerator = Rs. 9700

VAT = 6%

So, VAT = 6% of Rs. 9700

= Rs. 6/100 × 9700 = Rs. 582

So, the total amount one has to pay  = Rs. 9700 + Rs. 582

= Rs. 10,282

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Question 2:

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

ANSWER:

Let the list price of the watch be Rs.  x .

Then, x + 10/100. x = 825

x + 0.1 x = 825

1.1 x = 825

x = 825/1.1

= Rs. 750

Thus, the list price of the watch is Rs. 750.

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Question 3:

Aman bought a shirt for Rs 374.50 which includes 7% VAT. Find the list price of the shirt.

ANSWER:

Let the list price of the shirt be Rs.  x .

Then, x + 7/100. x = 374.50

x + 0.07 x = 374.50

1.07 x = 374.50

x = 374.50/1.07

= Rs. 350

Thus, the list price of the shirt is Rs. 350.Let 

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Question 4:

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

ANSWER:

Given,SP of the pair of shoes  =  Rs. 175

VAT = 7%

Therefore, VAT = 7% of Rs. 175

= 7/100 × 175

= Rs. 12.25

So, Rani has to pay Rs. 12.25 as VAT.

The net value of the pair of shoes = Rs. 175 + Rs. 12.25 = Rs. 187.25

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Question 5:

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

ANSWER:

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

2.5 x = 20 x = 8

Thus, Swarna paid 8% VAT on the pair of shoes.

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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.

ANSWER:

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

=  5/100 ×  5500

=  Rs 275

∴ new cost  =  Rs ( 5500 − 275)  =  Rs 5225

Now,VAT =  5% of 5225

= 5/100 ×  5225

= Rs 261.25

∴ amount to be paid for the goods  =  Rs ( 5225  +  261.25)

=  Rs 5486.25 

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Question 7:

The cost of furniture inclusive of VAT is Rs 7150. If the rate of VAT is 10%, find the original cost of the furniture.

ANSWER:

Cost of the furniture inclusive VAT = Rs. 7150

Let the original cost of the furniture be Rs.  x .

Cost of the furniture = 10% of  x + x

7150 = 1.10 x

x = 7150/1.10

= Rs. 6500

Thus, the original cost of the furniture is Rs. 6500. 

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Question 8:

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

ANSWER:

Cost of the refrigerator inclusive VAT = Rs. 13,750

Let the original cost of the furniture be Rs.  x .

Cost of the furniture = 10% of  x + x

13,750 = 1.10 x

x = 13,750/1.10

= Rs. 12,500

Thus, the original cost of the furniture is Rs. 12,500.

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Question 9:

A colour TV is available for Rs 13440 inclusive of VAT. If the original cost of TV is Rs 12000, find the rate of VAT.

ANSWER:

Cost price of the TV including VAT = Rs. 13440

Let the rate of VAT be  x %.

Cost of the TV = x % of 12000 + 12000

13440−12000 = 120 x

120 x = 1440

x = 1440/120

= 12

Thus, the rate of VAT on the colour TV is 12%.

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Question 10:

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

ANSWER:

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

Then,VAT = 7% of Rs.  x = Rs.7x/100

So, SP of the radio = Rs.( x + 7x/100) = Rs.107x/100

But, SP = Rs. 2568

So,107x/100 = 2568

x = Rs. 2400

Hence, the reduction needed in the price of the radio = Rs. (2568−2400) = Rs. 168. 

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Question 11:

Rajat goes to a departmental store and buys the following articles:

Calculate the total amount he has to pay to the store.

ANSWER:

Given,CP of 2 pair of shoes = Rs. 800 × 2 = Rs. 1600

Rate of VAT = 5%

So, VAT = 5% of Rs. 1600 = 5/100 × 1600 = Rs. 80.

Therefore, the amount Rajat needs to pay for 2 pair of shoes = Rs. (1600 + 80) = Rs.1680

Again,CP of 1 sewing machine = Rs. 1500

Rate of VAT = 6%

So, VAT = 6% of Rs. 1500 = 6/100 × 1500 = Rs. 90.

Therefore, the amount Rajat needs to pay for 1 sewing machine = Rs. (1500 + 90) = Rs.1590

Given,CP of 2 tea−sets = Rs. 650 × 2 = Rs. 1300

Rate of VAT = 4%

So, VAT = 4% of Rs. 1300 = 4/100 × 1300 = Rs. 52

Therefore, the amount Rajat needs to pay for 2 tea−sets = Rs. (1300 + 52) = Rs. 1352

Thus, the total amount Rajat needs to pay = Rs. (1680 + 1590 + 1352)

= Rs. 4622

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Question 12:

Ajit buys a motorcycle for Rs 17600 including value added tax . If the rate of VAT is 10%, what is the sale price of the motorcycle?

ANSWER:

Let the sale price of the motorcycle be Rs  x .

Cost including VAT = 10% of  x + x

17600  =  10/100  × x + x

17600  =  0.10 x +  x

1.10 x =  17600

x   =  17600/1.10      

=  16000

Thus, the sale price of the motorcycle is Rs 16000. 

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Question 13:

Manoj buys a lather coat costing Rs 900 at Rs 990 after paying the VAT. Calculate the rate of VAT charge on the coat.

ANSWER:

Let the rate of VAT be  x %. 

Then,VAT = Rs. (x/100 × 900) = Rs. 9 x

So,900 + 9 x = 9909 x = 90 x = 10

Thus, Manoj was charged 10% VAT on the leather jacket.

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Question 14:

Rakesh goes to a departmental store and purchases the following articles:
 (i) biscuits and bakery products costing Rs 50, VAT @ 5%,
 (ii) medicines costing Rs 90, VAT @ 10%,
 (iii) clothes costing Rs 400, VAT @ 1%, and
 (iv) cosmetics costing Rs 150, VAT @ 10%.
 Calculate the total amount to be paid by Rakesh to the store.

ANSWER:

(i) Cost of biscuits and bakery products = Rs. 50

VAT charged = 5%

So, VAT = 5% of Rs. 50 = 5/100 × 50 = Rs. 2.50

So, the total amount paid for biscuits and bakery products = Rs. (50 + 2.50) = Rs. 52.50

(ii) Cost of medicine = Rs. 90

VAT charged = 10%

So, VAT = 10% of Rs. 90 = 10/100 × 90 = Rs. 9

So, the total amount paid for medicines = Rs. (90 + 9) = Rs. 99

(iii) Cost of clothes = Rs. 400

VAT charged = 1%

So, VAT = 1% of Rs. 400 = 1100 × 400 = Rs. 4

So, the total amount paid for clothes = Rs. (400 + 4) = Rs. 404

(iv) Cost of cosmetics = Rs. 150

VAT charged = 10%

So, VAT = 10% of Rs. 150 = 10/100 × 150 = Rs. 15

So, the total amount paid for cosmetics = Rs. (150 + 15) = Rs. 165

Hence, the total amount Rakesh paid at the departmental store = Rs.(52.50 + 99 + 404 + 165) = Rs. 720.50

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Question 15:

Rajeeta purchased a set of cosmetics. She paid Rs 165 for it including VAT. If the rate of VAT is 10%, find the sale price of the set.

ANSWER:

Let the sale price of the set be Rs.  x

Given that the VAT charged is 10%.

Cost of the set = x + 10% of  x

165 = x + 0.10 x

165 = 1.10 x

x = 165/1.10

x = Rs. 150

Thus, the sale price of the set is Rs. 150.

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Question 16:

Sunita purchases a bicycle for Rs 660. She has paid a VAT of 10%. Find the list price of the bicycle?

ANSWER:

Let the sale price of the bicycle be Rs.  x . 

VAT charged = 10%

Again, 

Cost of the bicycle = x + 10% of  x

660 = x + 0.10 x

660 = 1.10 x

x = 660/1.10

x = Rs. 600

Thus, the list price of the bicycle is Rs. 600. 

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Question 17:

The sales price of a television, inclusive of VAT, is Rs 13,500. If VAT charged at the rate of 8% of the list price, find the list price of the television.

ANSWER:

Let the list price of the TV be Rs.  x .

VAT charged = 8%

Given, Cost price of the TV  =  Rs. 13,500

So, Cost price of the TV = x + 8% of  x 13,500 = x + 0.08 x

13,500 = 1.08 x

x = 13,500/1.08

x = Rs. 12,500

Thus, the list price of the TV is Rs. 12,500.

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Question 18:

Shikha purchased a car with a marked price of RS 210000 at a discount of 5%. If VAT is charged at the rate of 10%, find the amount Shikha had paid for purchasing the car.

ANSWER:

Marked price of the car = Rs. 2,10,000

Discount allowed = 5%

Therefore, discount = 5% of Rs. 2,10,000 = 5/100 × 2,10,000 = Rs. 10,500

So, Shikha gets a discount of Rs. 10,500.

 Therefore, cost of the car will be  = Marked price −Discount

Rs. ( 2,10,000−10,500) = Rs. 1,99,500

VAT = 10% of 1,99,500 = 10/100 × 199500 = Rs. 19,950

Thus, the amount paid by Shikha to purchase the car = Rs. (1,99,500 + 19,950) = Rs. 2,19,450

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Question 19:

Shruti bought a set of cosmetic items for Rs 345 including 15% value added ta x and a purse for Rs 110 including 10% VAT. What percent is the VAT charged on the whole transaction?

ANSWER:

Let the price of the cosmetic items be Rs.  x  and the price of the purse be Rs. y.

VAT = 15% of  x = 15x/100 = Rs. 3x/20

VAT = 10% of y = 10y/100 = Rs. y/10

So, SP of cosmetic items = x + 3 x 20 = Rs. 23 x 20

SP of purse = (y + y/10) = Rs. 11y/10

But the selling price of the cosmetic items and the purse is Rs. 345 and Rs. 110 respectively.

So,23x/20 = 345

 x = Rs. 300

and 11y/10 = 110

11y = 1100

y = Rs. 100

Total price = Rs. (300 + 100) = Rs. 400

Now,Let the VAT on the whole transaction be r%.

r% of 400 = r/100 × 400 = 4r

Total transaction = Rs. 345 + 110 = Rs. 455

So,4r + 400 = 455

4r = 55

r = 55/4 = 13.75

Thus, VAT charged on the whole transaction is 13.75%.

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Question 20:

List price of a cooler is Rs 2563. The rate of VAT is 10%. The customer requests the shopkeeper to allow a discount in the price of the cooler to such an e x tent that the price remains Rs 2563 inclusive of VAT. Find the descount in the price of the cooler.

ANSWER:

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

VAT = 10% of Rs  x = 10/100 × x

= Rs.  x/10

Therefore, SP of the cooler will be = Rs. (x + x/10) = Rs. 11x/10

But the SP is already given as Rs. 2563.

So, 2563 = 11x/10

11 x = 25630 

x = 25630/11 = Rs. 2330

Hence, discount allowed in the price of the cooler = Rs.(2563−2330) = Rs. 233. 

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Question 21:

List price of a washing machine is Rs 9000. If the dealer allows a discount of 5% on the cash payment, how much money will a customer pay to the dealer in cash, if the rate of VAT is 10%?

ANSWER:

List price of the washing machine = Rs. 9000

Discount allowed = 5%

Discount = 5% of Rs. 9000

= 5/100 × 9000 = Rs. 450

So, the cost of the washing machine = List price−Discount

= Rs. (9000−450) = Rs. 8550

VAT = 10% of Rs. 8550

= 10/100 × 8550 = Rs. 855

Thus, the customer has to pay = Rs. (8550 + 855) = Rs. 9405