[4 marks sum]

Question 14 Marks

A manufacturing company ‘P’ sells a Desert cooler to a dealer A for ₹ 8100 including sales tax (under VAT). The dealer A sells it to a dealer B for ₹ 8500 plus sales tax and the dealer B sells it to a consumer at a profit of ₹ 600. If the rate of sales tax (under VAT) is 8%, find
(i) the cost price of the cooler for dealer A.
(ii) the amount of tax received by the Government.
(iii) the amount which the consumer pays for the cooler.

Answer

Manufactures ' $P$ ' selling price for Desert cooler including sales tax(VAT)
$=\text { ₹ }8100$
Rate of sales tax (VAT) $=8 \%$
(i) $\therefore$ Sale price excluding VAT
$
\begin{aligned}
& =\frac{8100 \times 100}{100+8} \\
& =\frac{8100 \times 100}{108} \\
& =\text { ₹ }7500
\end{aligned}
$
Cost price of dealer $A=\text { ₹ } 7500$
and sale price of dealer $A=\text { ₹ }8500$
Gain
$
\begin{aligned}
& =\text { ₹ } 8500-\text { ₹ } 7500 \\
& =\text { ₹ } 1000
\end{aligned}
$
or cost price of dealer $B=\text { ₹ } 8500$
$
\text { Gain }=\text { ₹ } 600
$
S.P. of dealer B
$
\begin{aligned}
& =\text { ₹ } 8500+\text { ₹ }600 \\
& =\text { ₹ } 9100
\end{aligned}
$
Consumers cost price
$
\begin{aligned}
& =\text { ₹ }8500+\text { ₹ } 600 \\
& =\text { ₹ } 9100
\end{aligned}
$
(ii) Tax paid to the Govt.
$
\begin{aligned}
& =\text { ₹ }7500 \times \frac{8}{100}+\frac{1000 \times 8}{100}+\frac{600 \times 8}{100} \\
& =\text { ₹ } 600+\text { ₹ } 80+\text { ₹ } 48 \\
& =\text { ₹ } 728
\end{aligned}
$
The amount which the consumer pays
$
\begin{aligned}
& =\text { ₹ }7500+\text { ₹ } 1000+\text { ₹ } 600+\text { ₹ }728 \\
& =\text { ₹ }9828 .
\end{aligned}
$

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Question 24 Marks

A shopkeeper bought a TV at a discount of 30% of the listed price of ₹ 24000. The shopkeeper offers a discount of 10% of the listed price to his customer. If the VAT (Value Added Tax) is 10%, find the amount paid by the customer, the VAT to be paid by the shopkeeper.

Answer

$
\begin{aligned}
& \text { List price }=\text { ₹ } 24000 \\
& \text { Discount }=30 \% \\
& \text { S.P. } \\
& =24000-\frac{30}{100} \times 24000 \\
& =\text { ₹ }24000-\text { ₹ }7200 \\
& =\text { ₹ }16800
\end{aligned}
$
$
\begin{aligned}
& =24000-\frac{30}{100} \times 24000 \\
& =\text { ₹ } 24000-\text { ₹ } 7200 \\
& =\text { ₹ }16800
\end{aligned}
$VAT
$
\begin{aligned}
& =\text { ₹ } 16800 \times \frac{10}{100} \\
& =\text { ₹ } 1680
\end{aligned}
$
S.P. to customer
$
\begin{aligned}
& =\text { ₹ } 24000-24000 \times \frac{10}{100} \\
& =\text { ₹ } 24000-\text { ₹ } 2400 \\
& =\text { ₹ } 21600
\end{aligned}
$VAT
$
\begin{aligned}
& =\frac{10}{100} \times 21600 \\
& =\text { ₹ }2160
\end{aligned}
$
(i) Amount paid by customer
$
\begin{aligned}
& =\text { ₹ } 21600+\text { ₹ }2160 \\
& =\text { ₹ }23760
\end{aligned}
$
(ii) Total VAT to be paid by shopkeeper
$
\begin{aligned}
& =\text { ₹ }2160-\text { ₹ }1680 \\
& =\text { ₹ } 480 .
\end{aligned}
$

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Question 34 Marks

The printed price of an article is ₹ 60000. The wholesaler allows a discount of 20% to the shopkeeper. The shopkeeper sells the article to the customer at the printed price. Sales tax (under VAT) is charged at the rate of 6% at every stage. Find :
(i) the cost to the shopkeeper inclusive of tax.
(ii) VAT paid by the shopkeeper to the Government.
(iii) the cost to the customer inclusive of tax.

Answer

Printed price of an article $=\text { ₹ } 60000$
Rate of discount allowed $=20 \%$
Total discount
$
\begin{aligned}
& =\text { ₹ } 60000 \times \frac{20}{100} \\
& =\text { ₹ } 12000
\end{aligned}
$
S.P. after discount
$
\begin{aligned}
& =\text { ₹ } 60000-\text { ₹ }12000 \\
& =\text { ₹ }48000
\end{aligned}
$
Rate of VAT $=6 \%$
(i) Amount paid by the shopkeeper
$
\begin{aligned}
& =\text { ₹ } 48000+\text { ₹ }48000 \times \frac{6}{100} \\
& =\text { ₹ } 48000+\text { ₹ } 2880 \\
& =\text { ₹ }50880
\end{aligned}
$
(ii) The price at which the shopkeeper sold to the customer $=\text { ₹ } 60000$Profit
$
\begin{aligned}
& =\text { ₹ } 60000-\text { ₹ } 48000 \\
& =\text { ₹ }12000
\end{aligned}
$
VAT paid by the customer to the Govt.
$
\begin{aligned}
& =\text { ₹ }12000 \times \frac{6}{100} \\
& =\text { ₹ } 720
\end{aligned}
$
(iii) Total cost to the customer
$=\text { ₹ } 60000+$ VAT inclusive of tax
$
\begin{aligned}
& =\text { ₹ } 60000+\frac{60000 \times 6}{100} \\
& =\text { ₹ } 60000+\text { ₹ } 3600 \\
& =\text { ₹ } 63600 .
\end{aligned}
$

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Question 44 Marks

A shopkeeper buys a camera at a discount of 20% from the wholesaler, the printed price of the camera being ₹ 1600 and the rate of sales tax is 6%. The shopkeeper sells it to the buyer at the printed price and charges sales tax at the same rate. Find
(i) the price at which the camera can be bought.
(ii) the VAT (Value Added Tax) paid by the shopkeeper.

Answer

The printed price of the camera (MP) $=\text { ₹ } 1600$
Rate of discount $=20 \%$
$\therefore$ Sale price
$\begin{aligned}
& =\frac{ MP \times(100- D \%)}{100} \\
& =\frac{1600(100-20)}{100} \\
& =\frac{1600 \times 80}{100} \\
& =\text { ₹ }1280
\end{aligned}
$
Rate of S.T. $=6 \%$
$\therefore$ Total S.T.
$\begin{aligned}
& =\text { ₹ }\frac{1280 \times 6}{100} \\
& =\text { ₹ } 76.80
\end{aligned}
$
In second case,
Sale price $=\text { ₹ } 1600$,
Rate of sales tax $=6 \%$
$\therefore$ Total S.T.
$\begin{aligned}
& =\text { ₹ } \frac{1600 \times 6}{100} \\
& =\text { ₹ } 96
\end{aligned}
$
(i) Price of camera
$\begin{aligned}
& =\text { ₹ } 1600+\text { ₹ } 96 \\
& =\text { ₹ }1696
\end{aligned}
$
(ii) VAT paid by the shopkeeper
$\begin{aligned}
& =\text { ₹ } 96-\text { ₹ } 76.80 \\
& =\text { ₹ }19.20 .
\end{aligned}
$

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Question 54 Marks

In a particular tax period, Mr. Sunder Dass, a shopkeeper purchased goods worth ₹ 960000 and paid a total tax of ₹ 62750 (under VAT). During this period, his sales consisted of a taxable turnover of ₹ 400000 of goods taxable at 6% and ₹ 480000 for goods taxable at 12.5%. He also sold tax exempted goods worth ₹ 95640 in the same period. Calculate his tax liability (under VAT) for this period.

Answer

The cost price of good purchased by Sunder Dass $=\text { ₹ } 960000$
Tax paid (VAT) $=\text { ₹ } 62750$
Sale of goods worth $=\text { ₹ } 400000$
Rate of VAT $=6 \%$
$\therefore$ Total VAT
$
\begin{aligned}
& =400000 \times \frac{6}{100} \\
& =\text { ₹ } 24000
\end{aligned}
$
Sale of goods worth 480000
Rate of VAT $=12.5 \%$
$
=\frac{25}{2} \%
$
VAT paid
$
\begin{aligned}
& =\text { ₹ } 480000 \times \frac{25}{2 \times 100} \\
& =\text { ₹ } 60000
\end{aligned}
$
Sale of goods worth \text { ₹ }95640
Tax exempted
Total VAT
$
\begin{aligned}
& =\text { ₹ }24000+\text { ₹ } 60000 \\
& =\text { ₹ } 84000
\end{aligned}
$
Tax paid to Govt. (VAT)
$
=\text { ₹ } 62750
$
Tax liability
$=\text { ₹ } 84000-\text { ₹ }62750$
$=\text { ₹ } 21250$.

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Question 64 Marks

A shopkeeper buys an article for ₹ 12000 and marks up its price by 25%. The shopkeeper gives a discount of 10% on the marked up price. He gives a further off-season discount of 5% on the balance. But the sales tax (under VAT) is charged at 8% on the remaining price. Find :
(i) the amount of VAT that a customer has to pay.
(ii) the final price he has to pay for the article.

Answer

The cost price of an article $=\text { ₹ }12000$
Rate of mark up in price $=25 \%$
$\therefore$ Marked price
$
\begin{aligned}
& =\frac{\text { C.P. } \times(100+25)}{100} \\
& =\frac{12000 \times 125}{100} \\
& =\text { ₹ }15000
\end{aligned}
$
Rate of discount $=10 \%$
Rate off-season discount $=5 \%$
$\therefore$ Sale price
$
\begin{aligned}
& =\frac{\text { M.P. } \times(100-\text { discount } \%)}{100} \\
& =\frac{15000(100-10) \times(100-5)}{100 \times 100} \\
& =\text { ₹ } \frac{15000 \times 90 \times 95}{100 \times 100} \\
& =\text { ₹ }12825
\end{aligned}
$
Rate of sales tax $=8 \%$
$\therefore$ Amount of sales tax
$
\begin{aligned}
& =\text { ₹ }\frac{12825 \times 8}{100} \\
& =\text { ₹ } 1026
\end{aligned}
$
(i) Amount of sales tax
= \text { ₹ }1026
(ii) Price to be paid
$
\begin{aligned}
& =\text { ₹ }12825+\text { ₹ } 1026 \\
& =\text { ₹ } 13851 .
\end{aligned}
$

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Question 74 Marks

Kiran purchases an article for ₹ 5, 400 which includes a 10% rebate on the marked price and 20% sales tax (under VAT) on the remaining price. Find the marked price of the article.

Answer

Let the market price of the article be $\text { ₹ } x$
Then, rebate
$
\begin{aligned}
& =10 \% \text { of } \text { ₹ } x \\
& =\text { ₹ } \frac{x}{10}
\end{aligned}
$
Price after rebate
$
\begin{aligned}
& =\text { ₹ }\left(x-\frac{x}{10}\right) \\
& =\text { ₹ } \frac{9 x}{10}
\end{aligned}
$
$
\begin{aligned}
& \text { Sales tax } \\
& =20 \% \text { of } \text { ₹ }\frac{9 x}{10} \\
& =\text { ₹ } \frac{9 x}{10} \times \frac{20}{100} \\
& =\text { ₹ } \frac{9 x}{50}
\end{aligned}
$
$\therefore S P$ of the article
$
\begin{aligned}
& =\text { ₹ }\left(\frac{9 x}{10}+\frac{9 x}{50}\right) \\
& =\frac{45 x+9 x}{50} \\
& =\text { ₹ } \frac{54 x}{50} \\
& =\text { ₹ }\frac{27 x}{25}
\end{aligned}
$
But $SP =\text { ₹ }5400$... (given)
$
\begin{aligned}
& \therefore \frac{27 x}{25}=\text { ₹ } 5400 \\
& \Rightarrow x=\frac{5400 \times 25}{27} \\
& =200 \times x 25 \\
& =\text { ₹ } 5000
\end{aligned}
$
Hence, market price of the article is $\text { ₹ } 5000$.

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Question 84 Marks

A manufacturer marks an article for ₹ 5000. He sells it to a wholesaler at a discount of 25% on the marked price and the wholesaler sells it to a retailer at a discount of 15% on the marked price. The retailer sells it to a consumer at the marked price and at each stage, the VAT is 8%.
Calculate the amount of VAT received by the Government from :
(i) the wholesaler.
(ii) the retailer.

Answer

Marked price (M.P.) of an article $=\text { ₹ } 5000$
Discount is given to the wholesaler $=25 \%$
Cost price of wholesaler or S.P. of the manufacturer
$
\begin{aligned}
& =\text { ₹ }\frac{5000(100-25)}{100} \\
& =\text { ₹ } \frac{5000 \times 75}{100} \\
& =\text { ₹ } 3750
\end{aligned}
$
Discount is given to the retailer or S.P. of the wholesaler
$
\begin{aligned}
& =\text { ₹ } \frac{5000 \times(100-15)}{100} \\
& =\text { ₹ }\frac{5000 \times 85}{100} \\
& =\text { ₹ } 4250^{\circ}
\end{aligned}
$
Cost price of the customers $=\text { ₹ } 5000$
Rate of VAT $=8 \%$
VAT for the manufacture
$
\begin{aligned}
& =\frac{3750 \times 8}{100} \\
& =\text { ₹ } 300
\end{aligned}
$
VAT for the wholesaler
$
\begin{aligned}
& =\frac{4250 \times 8}{100} \\
& =\text { ₹ } 340
\end{aligned}
$
and VAT for the retailer
$
\begin{aligned}
& =\frac{5000 \times 8}{100} \\
& =\text { ₹ }400
\end{aligned}
$
(i) VAT received from the wholesaler
$
\begin{aligned}
& =\text { ₹ } 340-\text { ₹ } 300 \\
& =\text { ₹ } 40
\end{aligned}
$
(ii) and VAT received by the retailer
$
\begin{aligned}
& =\text { ₹ } 400-\text { ₹ } 340 \\
& =\text { ₹ } 60 .
\end{aligned}
$

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Question 94 Marks

A shopkeeper buys an article at a discount of 30% and pays sales tax at the rate of 6%. The shopkeeper sells the article to a consumer at 10% discount on the list price and charges sales tax at the’ same rate. If the list price of the article is ₹3000, find the price inclusive of sales tax paid by the shopkeeper.

Answer

List price of an article $=\text { ₹ } 3000$
Rate of discount $=30 \%$
and rate of S.T. $=6 \%$
Total discount
$
\text { = ₹ } 3000 \times \frac{30}{100}=\text { ₹ } 900
$
$\therefore$ S.P. of manufactures or
C.P. of the shopkeeper
$
\begin{aligned}
& =\text { ₹ } 3000 \text { - \text { ₹ }900 } \\
& =\text { ₹ } 2100 \\
& \text { S.T. =\text { ₹ } } 2100 \times \frac{6}{100}=\text { ₹ } 126
\end{aligned}
$
Rebate given to consumer $=10 \%$
and C.P. of the consumer
$
\begin{aligned}
& =\text { ₹ }\frac{3000 \times(100-10)}{100} \\
& =\text { ₹ } \frac{3000 \times 90}{100} \\
& =\text { ₹ } 2700
\end{aligned}
$
(i) S.T. paid by shopkeeper $=\text { ₹ } 126$
Total cost pre of the shopkeeper
$
\begin{aligned}
& =\text { ₹ } 2100+126 \\
& =\text { ₹ }2226
\end{aligned}
$
(ii) S.T. for consumer
$
\begin{aligned}
& =2700 \times \frac{6}{100} \\
& =\text { ₹ } 162
\end{aligned}
$
$\therefore$ Total cost price paid by the consumer
$
\begin{aligned}
& =\text { ₹ } 2700+\text { ₹ } 162 \\
& =\text { ₹ }2862
\end{aligned}
$
(iii) VAT paid by the shopkeeper
$
\begin{aligned}
& =\text { ₹ } 162-\text { ₹ } 126 \\
& =\text { ₹ } 36 .
\end{aligned}
$

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Question 104 Marks

In the tax period ended March 2015, M/S Hari Singh & Sons purchased floor tiles worth ₹ 800000 taxable at 7.5% and sanitary fittings worth ₹ 750000 taxable at 10%. During this period, the sales turnover for floor tiles and sanitary fittings is worth ₹ 840000 and ₹ 920000 respectively. However, the floor tiles worth ₹ 60000 were returned by the firm during the same period. Calculate the tax liability (under VAT) of the firm for this tax period.

Answer

Cost of floor tiles $=\text { ₹ } 800000$
Rate of tax $=7.5 \%$
$
\begin{aligned}
& =\frac{15}{2} \% \\
& \therefore \text { VAT }
\end{aligned}
$
$
\begin{aligned}
& =\frac{800000 \times 15}{100 \times 2} \\
& =\text { ₹ } 60000
\end{aligned}
$
Cost of sanitary fittings $=\text { ₹ } 750000$
Rate of VAT $=10 \%$
Total VAT
$
\begin{aligned}
& =\text { ₹ }750000 \times \frac{10}{100}=\text { ₹ } 75000 \\
& \therefore \text { Total input } \\
& =\text { ₹ } 60000+\text { ₹ }75000 \\
& =\text { ₹ } 135000
\end{aligned}
$
On the sale of floor tiles for $=\text { ₹ } 840000$
Rate of VAT $=\frac{15}{2} \%$
Total VAT
$
\begin{aligned}
& =840000 \times \frac{15}{100 \times 2} \\
& =\text { ₹ } 63000
\end{aligned}
$
and on sale of sanitary fittings = \text { ₹ }920000
Rate of VAT $=10 \%$
$\therefore$ Total VAT
= \text { ₹ } $920000 \times \frac{10}{100}=\text { ₹ } 92000$
Total input tax
$
\begin{aligned}
& =\text { ₹ } 63000+\text { ₹ } 92000 \\
& =\text { ₹ }155000
\end{aligned}
$
Return of floor tiles worth
$
=\text { ₹ } 60000
$
Liability of tax of the firm
$=155000-(135000+4500)$
$=\text { ₹ } 155000$ - \text { ₹ }139500
$=\text { ₹ } 15500$.

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Question 114 Marks

A manufacturer listed the price of his goods at ₹ 160 per article. He allowed a discount of 25% to a wholesaler who in his turn allowed a discount of 20% on the listed price to a retailer. The rate of sales tax on the goods is 10%. If the retailer sells one article to a consumer at a discount of 5% on the listed price, then find
(i) the VAT paid by the wholesaler.
(ii) the VAT paid by the retailer.
(iii) the VAT received by the Government.

Answer

List price $( MP )$ of the goods $=\text { ₹ } 160$ per article
Rate of discount $=25 \%$
S.P.
$
\begin{aligned}
& =\frac{ MP \times(100- D \%)}{100} \\
& =\text { ₹ }\frac{160(100-25)}{100} \\
& =\text { ₹ } \frac{160 \times 75}{100} \\
& =\text { ₹ } 120
\end{aligned}
$
Rate of VAT $=10 \%$
$\therefore$ Total VAT
$
\begin{aligned}
& =\text { ₹ } \frac{120 \times 10}{100} \\
& =\text { ₹ }12
\end{aligned}
$
Now S.P. of wholesaler $=\text { ₹ } 160$
Rate of discount $=20 \%$
$\therefore$ Net S.P.
$
\begin{aligned}
& =\text { ₹ } \frac{160 \times(100-20)}{100} \\
& =\text { ₹ } \frac{160 \times 80}{100} \\
& =\text { ₹ }128
\end{aligned}
$
Rate of VAT $=10 \%$
$\therefore$ Total VAT
$
=\text { ₹ } \frac{128 \times 10}{100}
$
$=\text { ₹ }12.80$
Total S.P.
$=\text { ₹ } 128+\text { ₹ }12.80$
$=\text { ₹ }140.8$
Now S.P. of the retailer $=\text { ₹ } 160$
Net S.P.
$
\begin{aligned}
& =\text { ₹ } \frac{160 \times(100-5)}{100} \\
& =\text { ₹ } \frac{160 \times 95}{100} \\
& =\text { ₹ } 152
\end{aligned}
$
VAT at the rate of $10 \%$
$
\begin{aligned}
& =\text { ₹ } \frac{152 \times 10}{100} \\
& =\text { ₹ } 15.20
\end{aligned}
$
(i) VAT paid by the wholesaler
$
\begin{aligned}
& =\text { ₹ } 12.80-\text { ₹ } 12 \\
& =\text { ₹ }0.80
\end{aligned}
$
(ii) VAT paid by the retailer
$
\begin{aligned}
& =15.20-12.80 \\
& =\text { ₹ } 2.40
\end{aligned}
$
(iii) Total VAT paid to the Govt.
$
=\text { ₹ } 15.20 \text {. }
$

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Question 124 Marks

A retailer buys an article at a discount of 15% on the printed price from a wholesaler. He marks up the price by 10%. Due to competition in the market, he allows a discount of 5% to a buyer. If the buyer pays ₹451.44 for the article inclusive of sales tax (under VAT) at 8%, find :
(i) the printed price of the article
(ii) the profit percentage of the retailer.

Answer

(i) Let the printed price of the article = ₹100
Then, retailer’s cost price
= ₹100-₹15 = ₹85
Now, marked price for the retailer
= ₹100 + ₹10 = ₹110
Rate of discount allowed = 5%
∴ Sale price
$\begin{aligned}
& =\text { ₹ } \frac{110 \times(100-5)}{100} \\
& =\text { ₹ } \frac{110 \times 95}{100} \\
& =\text { ₹ } \frac{1045}{10}
\end{aligned}$
$\therefore$ Sale price including sales tax
$\begin{aligned}
& =\text { ₹ } \frac{1045}{10} \times \frac{100+8}{100} \\
& =\text₹ \frac{1045 \times 108}{1000}
\end{aligned}$
Now, if the buyers pays ₹ $\frac{1045 \times 108}{1000}$
then printed price $=\text { ₹ }100$
and if buyer pays $\text { ₹ } 451.44$, then printed price
$
\begin{aligned}
& =\text { ₹ }\frac{100 \times 451.44 \times 1000}{1045 \times 105} \\
& =\frac{100 \times 45144 \times 1000}{100 \times 1045 \times 108} \\
& =\text { ₹ } 400
\end{aligned}
$
$\therefore$ Printed price $=\text { ₹ }400$
(ii) Now, gain of the retailer
$
=\text { S.P. }- \text { C.P. }
$
$
=\text { ₹ } \frac{1045}{10}-\frac{85}{1}
$
$
=\frac{1045-850}{10}
$
$
=\text { ₹ } \frac{195}{10}
$
$\therefore$ Gain percent
$
=\frac{\text { Total gain } \times 100}{\text { C.P. }}
$
$
=\frac{195 \times 100}{10 \times 85}
$
$
=\frac{390}{17}
$
$
=22 \frac{16}{17} \%
$

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Mathematics [4 marks sum]

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