myhelper: RD Sharma solution class 8 chapter 13 Profit ,Discount and Value Added Tax(VAT) Exercise 13.3

Exercise 13.3

Page-13.32

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?

Answer 1:

$List price of t h e refrigerator = Rs . 9700 VAT = 6 % So, VAT = 6 % of Rs . 9700 = Rs . \frac{6}{100} \times 9700 = Rs . 582 So, t h e total amount o n e h a s to pay = Rs . 9700 + Rs . 582 = Rs . 10, 282$

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 2:

$Let the list price o f t h e w a t c h be Rs . x . Then, x + \frac{10}{100} x = 825 x + 0.1 x = 825 1.1 x = 825 x = \frac{825}{1.1} = R s . 750 Thus, t h e list price o f t h e w a t c h is Rs . 750 .$

Question 3:

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

Answer 3:

$Let the list price o f t h e s h i r t be Rs . x . Then, x + \frac{7}{100} x = 374.50 x + 0.07 x = 374.50 1.07 x = 374.50 x = \frac{374.50}{1.07} = R s . 350 Thus, t h e list price o f t h e s h i r t is Rs . 350 .$

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 4:

$G i v e n, S P o f t h e p a i r o f s h o e s = R s . 175 VAT = 7 % T h e r e f o r e, VAT = 7 % of Rs . 175 = \frac{7}{100} \times 175 = Rs . 12.25 So, R a n i h a s to pay Rs . 12.25 as VAT . T h e n e t v a l u e of the pair of shoes = Rs . 175 + Rs . 12.25 = Rs . 187.25$

Question 5:

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

Answer 5:

$G i v e n, A m o u n t p a i d b y S w a r n a f o r a p a i r o f s h o e s = R s . 250 V A T p a i d b y h e r = R s . 20 Let the rate of VAT be x % . Then, x % of 250 = 20 \frac{x}{100} \times 250 = 20 2.5 x = 20 x = 8 Thus, S w a r n a p a i d 8 % V A T o n t h e p a i r o f s h o e s .$

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 6:

$Price after getting a rebate of 5 % on Rs 5500 = 5 % of 5500 = \frac{5}{100} \times 5500 = Rs 275 ∴ new cost = Rs (5500 - 275) = Rs 5225 Now, VAT = 5 % of 5225 = \frac{5}{100} \times 5225 = Rs 261.25 ∴ a mount to be paid for the goods = Rs (5225 + 261.25) = Rs 5486.25$

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 7:

$Cost of the furniture inclusive VAT = Rs . 7150 Let the original cost of the furniture be Rs . x . Cost of the furniture = 10 % of x + x 7150 = 1.10 x x = \frac{7150}{1.10} = Rs . 6500 Thus, the original cost of the furniture is Rs . 6500 .$

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 8:

$Cost of the refrigerator inclusive VAT = Rs . 13, 750 Let the original cost of the furniture be Rs . x . Cost of the furniture = 10 % of x + x 13, 750 = 1.10 x x = \frac{13, 750}{1.10} = Rs . 12, 500 Thus, the original cost of the furniture is Rs . 12, 500 .$

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 9:

$Cost p r i c e of the TV inclu d i n g VAT = Rs . 13440 Let the rate of VAT be x % . Cost of the TV = x % of 12000 + 12000 13440 - 12000 = 120 x 120 x = 1440 x = \frac{1440}{120} = 12 Thus, the rate of VAT o n t h e c o l o u r T V is 12 % .$

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 10:

$Let the reduced price, excluding VAT, of the radio be Rs x . Then, VAT = 7 % of Rs . x = Rs . \frac{7 x}{100} So, SP of the radio = Rs . (x + \frac{7 x}{100}) = Rs . \frac{107 x}{100} But, SP = Rs . 2568 So, \frac{107 x}{100} = 2568 x = Rs . 2400 Hence, the reduction needed in the price of the radio = Rs . (2568 - 2400) = Rs . 168 .$

Question 11:

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

Item	Price per item	Rate of VAT
2 Pairs of shoes 1Sewing machine 2 Tea-sets	Rs 800 Rs 1500 Rs 650	5% 6% 4%

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

Answer 11:

$G i v e n, CP of 2 pair of shoes = Rs . 800 \times 2 = Rs . 1600 Rate of VAT = 5 % So, VAT = 5 % of Rs . 1600 = \frac{5}{100} \times 1600 = Rs . 80 . T h e r e f o r e, t h e amount R a j a t n e e d s t o pa y for 2 pair of shoes = Rs . (1600 + 80) = Rs . 1680 A g a i n, CP of 1 sewing machine = Rs . 1500 Rate of VAT = 6 % So, VAT = 6 % of Rs . 1500 = \frac{6}{100} \times 1500 = Rs . 90 . T h e r e f o r e, t h e amount R a j a t n e e d s t o pa y for 1 sewing machine = Rs . (1500 + 90) = Rs . 1590 G i v e n, CP of 2 t e a - sets = Rs . 650 \times 2 = Rs . 1300 Rate of VAT = 4 % So, VAT = 4 % of Rs . 1300 = \frac{4}{100} \times 1300 = Rs . 52 T h e r e f o r e, t h e amount R a j a t n e e d s t o pa y for 2 t ea - sets = Rs . (1300 + 52) = Rs . 1352 Thus, t h e total amount R a j a t n e e d s to pay = Rs . (1680 + 1590 + 1352) = Rs . 4622$

Page-13.33

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 12:

$Let the sale price of the motorcycle be Rs x . Cost including VAT = 10 % of x + x 17600 = \frac{10}{100} \times x + x 17600 = 0.10 x + x 1.10 x = 17600 x = \frac{17600}{1.10} = 16000 Thu s, the sale price of the motorcycle is Rs 16000 .$

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 13:

$Let the rate of VAT be x % . Then, VAT = Rs . (\frac{x}{100} \times 900) = Rs . 9 x S o, 900 + 9 x = 990 9 x = 90 x = 10 Thus, M a n o j w a s c h a r g e d 10 % VAT o n t h e l e a t h e r j a c k e t .$

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 14:

$(i) C o s t o f b iscuits and bakery products = Rs . 50 VAT c h a r g e d = 5 % So, VAT = 5 % of Rs . 50 = \frac{5}{100} \times 50 = Rs . 2.50 So, t h e t o t a l amount paid for biscuits and bakery products = Rs . (50 + 2.50) = Rs . 52.50 (ii) C ost o f m e d i c i n e = Rs . 90 VAT c h a r g e d = 10 % So, VAT = 10 % of Rs . 90 = \frac{10}{100} \times 90 = Rs . 9 So, t h e t o t a l amount paid for medicines = Rs . (90 + 9) = Rs . 99 (iii) C ost o f c l o t h e s = Rs . 400 VAT c h a r g e d = 1 % So, VAT = 1 % of Rs . 400 = \frac{1}{100} \times 400 = Rs . 4 So, t h e t o t a l amount paid for clothes = Rs . (400 + 4) = Rs . 404 (iv) C ost o f \cos m e t i c s = Rs . 150 VAT c h a r g e d = 10 % So, VAT = 10 % of Rs . 150 = \frac{10}{100} \times 150 = Rs . 15 So, t h e t o t a l amount paid for cosmetics = Rs . (150 + 15) = Rs . 165 Hence, t h e total amount Rakesh p a i d a t t h e d e p a r t m e n t a l s t o r e = Rs . (52.50 + 99 + 404 + 165) = Rs . 720.50$

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 15:

$Let the sale price of the set be Rs . x G i v e n t h a t t h e VA T c h a r g e d i s 10 % . Cost o f t h e s e t = x + 10 % of x 165 = x + 0.10 x 165 = 1.10 x x = \frac{165}{1.10} x = R s . 150 Thus, t h e s a l e p r i c e o f t h e s e t is Rs . 150 .$

Question 16:

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

Answer 16:

$Let the sale price of the bicycle be Rs . x . VAT c h a r g e d = 10 % A g a i n, Cost o f t h e b i c y c l e = x + 10 % of x 660 = x + 0.10 x 660 = 1.10 x x = \frac{660}{1.10} x = R s . 600 Thus, t h e list p r i c e o f t h e bicycle is Rs . 600 .$

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 17:

$Let the list price of the TV be Rs . x . VAT c h a r g e d = 8 % G i v e n, C o s t p r i c e o f t h e T V = R s . 13, 500 S o, Cost p r i c e o f t h e T V = x + 8 % of x 13, 500 = x + 0.08 x 13, 500 = 1.08 x x = \frac{13, 500}{1.08} x = R s . 12, 500 Thus, t h e list p r i c e o f t h e TV is Rs . 12, 500 .$

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 18:

$Marked price o f t h e c a r = Rs . 2, 10, 000 D iscount a l l o w e d = 5 % T h e r e f o r e, d i s c o u n t = 5 % of Rs . 2, 10, 000 = \frac{5}{100} \times 2, 10, 000 = Rs . 10, 500 S o, S hikha get s a d i s c o u n t o f Rs . 10, 500 . T h e r e f o r e, c ost of t h e car will be = Marked price - D iscount Rs . (2, 10, 000 - 10, 500) = Rs . 1, 99, 500 VA T = 10 % of 1, 99, 500 = \frac{10}{100} \times 199500 = Rs . 19, 950 Thus, t h e a mount paid by Shikha to purchase the car = Rs . (1, 99, 500 + 19, 950) = Rs . 2, 19, 450$

Question 19:

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

Answer 19:

$Let the price of t h e cosmetic items be R s . x and t h e p rice of t h e purse be Rs . y . VAT = 15 % of x = \frac{15 x}{100} = R s . \frac{3 x}{20} VAT = 10 % of y = \frac{10 y}{100} = R s . \frac{y}{10} So, SP of cosmetic items = x + \frac{3 x}{20} = R s . \frac{23 x}{20} SP of purse = (y + \frac{y}{10}) = R s . \frac{11 y}{10} But t h e selling price of t h e cosmetic i t e m s and t h e purse i s Rs . 345 and Rs . 110 r e s p e c t i v e l y . So, \frac{23 x}{20} = 345 x = R s . 300 and \frac{11 y}{10} = 110 11 y = 1100 y = R s . 100 Total price = Rs . (300 + 100) = Rs . 400 N o w, L e t t h e VAT on the whole transaction be r % . r % of 400 = \frac{r}{100} \times 400 = 4 r T otal transaction = R s . 345 + 110 = R s . 455 So, 4 r + 400 = 455 4 r = 55 r = \frac{55}{4} = 13.75 Thus, VAT c h a r g e d on t h e whole transaction is 13.75 % .$

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 extent that the price remains Rs 2563 inclusive of VAT. Find the descount in the price of the cooler.

Answer 20:

$Let the reduced price o f t h e c o o l e r, excluding VAT, be Rs . x . VAT = 10 % of Rs x = \frac{10}{100} \times x = R s . \frac{x}{10} T h e r e f o r e, SP of the cooler will be = Rs . (x + \frac{x}{10}) = Rs . \frac{11 x}{10} But t h e SP i s a l r e a d y given a s Rs . 2563 . So, 2563 = \frac{11 x}{10} 11 x = 25630 x = \frac{25630}{11} = Rs . 2330 Hence, d iscount a l l o w e d in the price of the cooler = Rs . (2563 - 2330) = Rs . 233 .$

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 21:

$List price o f t h e w a s h i n g m a c h i n e = Rs . 9000 Discount a l l o w e d = 5 % Discount = 5 % of Rs . 9000 = \frac{5}{100} \times 9000 = Rs . 450 So, t h e c ost of the washing machine = List price - D iscount = Rs . (9000 - 450) = Rs . 8550 VAT = 10 % of Rs . 8550 = \frac{10}{100} \times 8550 = Rs . 855 Thus, t h e customer has to pay = Rs . (8550 + 855) = Rs . 9405$

RD Sharma solution class 8 chapter 13 Profit ,Discount and Value Added Tax(VAT) Exercise 13.3