[3 marks sum]

Question 13 Marks

A shopkeeper buys an article whose list price is ₹ 800 at some rate of discount from a wholesaler. He sells the article to a consumer at the list price and charges sales tax at the prescribed rate of 7.5%. If the shopkeeper has to pay a VAT of ₹ 6, find the rate of discount at which he bought the article from the wholesaler.

Answer

List price (MP) of an article $=\text { ₹ } 800$
S.P. of the shopkeeper $=\text { ₹ } 800$
Rate of VAT $=7.5 \%$
Total VAT
$
\begin{aligned}
& =\text { ₹ }\frac{800 \times 7.5}{100} \\
& =\text { ₹ } 60
\end{aligned}
$
VAT paid by the shopkeeper $=\text { ₹ } 6$
VAT paid by the wholeseller
$
\begin{aligned}
& =\text { ₹ } 60-\text { ₹ } 6 \\
& =\text { ₹ }54
\end{aligned}
$
Rate of VAT $=7.5 \%$
S.P. of wholeseller
$
\begin{aligned}
& =\frac{54 \times 100}{7.5} \\
& =\frac{54 \times 10 \times 100}{75} \\
& =\text { ₹ } 720
\end{aligned}
$
Total discount
$
\begin{aligned}
& =\text { ₹ } 800-\text { ₹ }720 \\
& =\text { ₹ }80
\end{aligned}
$
Rate of discount
$
\begin{aligned}
& =\frac{80 \times 100}{800} \\
& =10 \%
\end{aligned}
$

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Question 23 Marks

A shopkeeper sells an article at the listed price of ₹ 1500 and the rate of VAT is 12% at each stage of the sale. If the shopkeeper pays a VAT of ₹ 36 to the Government, what was the amount inclusive of tax at which the shopkeeper purchased the articles from the wholesaler?

Answer

List price (M.P.) of an article $=\text { ₹ } 1500$
Rate of VAT $=12 \%$
Total VAT
$
\begin{aligned}
& =\text { ₹ } \frac{1500 \times 12}{100} \\
& =\text { ₹ }180
\end{aligned}
$
But VAT paid by the shopkeeper $=\text { ₹ } 36$
Total VAT paid by wholeseller
$
\begin{aligned}
& =\text { ₹ }180 \text { - ₹ } 36 \\
& =\text { ₹ }144
\end{aligned}
$
Rate of VAT $=12 \%$
S.P. of the whole seller
$
\begin{aligned}
& =\frac{144 \times 100}{12} \\
& =\text { ₹ } 1200
\end{aligned}
$
Total amount paid by the wholeseller including VAT
$
\begin{aligned}
& =\text { ₹ } 1200+\text { ₹ } 144 \\
& =\text { ₹ } 1344 .
\end{aligned}
$

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Question 33 Marks

A manufacturer buys raw material for ₹ 40000 and pays sales tax at the rate of 4%. He sells the ready stock for ₹ 78000 and charges sales tax at the rate of 7.5%. Find the VAT paid by the manufacturer.

Answer

The cost price of raw material $=\text { ₹ } 40000$
Rate of sales tax $=4 \%$
Total tax
$=\text { ₹ } \frac{40000 \times 4}{100}=\text { ₹ }1600$
Selling price $=\text { ₹ } 78000$
Rate of sales tax $=7.5 \%$
$\therefore$ Total tax
$=\text { ₹ } \frac{78000 \times 7.5}{100}$
$\begin{aligned}
& =\text { ₹ } \frac{78000 \times 75}{100 \times 10} \\
& =\text { ₹ } 5850\end{aligned}$
VAT paid by the manufacturer
$\begin{aligned}
& =\text { ₹ }5850-\text { ₹ } 1600 \\
& =\text { ₹ }4250 .
\end{aligned}$

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Question 43 Marks

A manufacturing company sells a T.V. to a trader A for ₹ 18000. Trader A sells it to a trader B at a point of ₹ 750 and trader B sells it to a consumer at a profit of ₹ 900. If the rate of sales tax (under VAT) is 10%, find
(i) the amount of tax received by the Government.
(ii) the amount paid by the consumer for the T.V.

Answer

The sale price of a T.V. to trader A = ₹ 18000
Rate of VAT tax = 10%
∴ Amount of VAT
$=18000 \times \frac{10}{100}=\text { ₹ } 1800$
he gain of A = ₹750
∴ VAT on gain
$=\text { ₹ } \frac{750 \times 10}{100}=\text { ₹ } 75$
Gain of trader B = ₹900
VAT tax paid
$=\frac{900 \times 10}{100}=\text { ₹ } 90$
(i) Total tax paid to Govt.
= ₹ (I800 + 75 + 90)
= ₹ 1965
(ii) Amount paid by the consumer to trader B
= ₹ 18000 + 750 + 900 + Tax 1965
= ₹ 21615.

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Question 53 Marks

Mukerjee purchased a movie camera for ₹27468. which includes 10% rebate on the list price and then 9% sales tax (under VAT) on the remaining price. Find the list price of the movie camera.

Answer

Let list price of the movie camera $=x$
Rebate $=10 \%$
Price after rebate
$
\begin{aligned}
& =x \times \frac{100-10}{100} \\
& =x \times \frac{90}{100}
\end{aligned}
$
Sale tax $=9 \%$
Sale price
$
\begin{aligned}
& =\frac{90}{100} x \times \frac{100+9}{100} \\
& =\frac{90}{100} x \times \frac{109}{100} \\
& =\frac{981}{1000} x \\
& \therefore \frac{981}{1000} x=\text { ₹ } 27468 \\
& \Rightarrow x=\frac{27468 \times 1000}{981} \\
& \therefore x \\
& =28 \times 100 \\
& =\text { ₹ }28000
\end{aligned}
$
$\therefore$ List price of movie camera $=\text { ₹ } 28000$.

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Question 63 Marks

The marked price of an article is ₹7500. A shopkeeper sells the article to a consumer at the marked prices and charges sales tax at . the rate of 7%. If the shopkeeper pays a VAT of ₹105, find the price inclusive of sales tax of the article which the shopkeeper paid to the wholesaler.

Answer

Marked price of an article $=\text { ₹ }7500$
Rate of S.T. $=7 \%$
$\therefore$ Total tax
$
\begin{aligned}
& =\text { ₹ } \frac{7500 \times 7}{100} \\
& =\text { ₹ }525
\end{aligned}
$
and VAT paid by the shopkeeper $=\text { ₹ } 105$
Difference of tax(VAT)
$
=\text { ₹ }525-\text { ₹ } 105
$
$
=\text { ₹ } 420
$
$\therefore$ Tax
$=\text { ₹ } 420$ and rate $=7 \%$
$\therefore$ C.P. of the shopkeeper
$
\begin{aligned}
& =\text { ₹ } \frac{420 \times 100}{7} \\
& =\text { ₹ }6000
\end{aligned}
$
and total C.P. paid by the shopkeeper
$
\begin{aligned}
& =\text { ₹ } 6000+\text { ₹ } 420 \\
& =\text { ₹ } 6420 .
\end{aligned}
$

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Question 73 Marks

A manufacturing company sold an article to its distributor for ₹22000 including VAT. The distributor sold the article to a dealer for ₹22000 excluding tax and the dealer sold it to a consumer for ₹25000 plus tax (under VAT). If the rate of sales tax (under VAT) at each stage is 10%, find :
(i) the sale price of the article for the manufacturing company.
(ii) the amount of VAT paid by the dealer.

Answer

S.P. of an article for a manufacturer $=\text { ₹ } 22000$ including VAT
C.P. for the distributor $\text { ₹ }22000$
Rate of VAT $=10 \%$
S.P. for the distributor of \text { ₹ } 22000 excluding VAT
S.P. for the consumer
$
\begin{aligned}
& =\text { ₹ }25000+\operatorname{Tax}(\text { VAT }) \\
& =\text { ₹ }25000+10 \% \text { of } \text { ₹ } 25000 \\
& =\text { ₹ }25000+\text { ₹ } 2500 \\
& =\text { ₹ }27500
\end{aligned}
$
(i) Sale price for the manufacturer
$
\begin{aligned}
& =\text { ₹ }22000 \times \frac{100}{100+10} \\
& =\text { ₹ } 22000 \times \frac{100}{110} \\
& =\text { ₹ } 20000
\end{aligned}
$
(ii) Amount of VAT paid by the dealer
$
\begin{aligned}
& =\text { ₹ } 25000 \times \frac{10}{100} \\
& =\text { ₹ } 2500 .
\end{aligned}
$

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Question 83 Marks

A shopkeeper bought a washing machine at a discount of 20% from a wholesaler, the printed price of the washing machine being Rs. 18,000. The shopkeeper sells it to a consumer at a discount of 10% on the printed price. If the rate of sales tax is 8%, find:
(i) the VAT paid by the shopkeeper.
(ii) the total amount that the consumer pays for the washing machine

Answer

(i) S.P. of washing machine
$
\begin{aligned}
& =\left(1-\frac{10}{100}\right) \times\text { ₹ }18000 \\
& =\frac{9}{100} \times 18000=\text { ₹ }16200
\end{aligned}
$
Sale tax
$
=8 \% \text { of } \text { ₹ } 16200
$
$
=\frac{8}{100} \times 16200=\text { ₹ } 1296
$
Printed price $=\text { ₹ } 18000$
Price paid by shopkeeper
$
\begin{aligned}
& =\left(1-\frac{20}{100}\right) \times \text { ₹ } 18000 \\
& =\frac{8}{100} \times \text { ₹ }14400=\text { ₹ }1152
\end{aligned}
$
(i) VAT paid by shopkeeper
$=$ Tax charged - Tax paid
$=\text { ₹ } 1296-\text { ₹ }1152$
$=\text { ₹ } 144$
(ii) Price paid by customer
$
\begin{aligned}
& =\text { ₹ } 16200+\text { ₹ } 1296 \\
& =\text { ₹ } 17496 .
\end{aligned}
$

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Mathematics [3 marks sum]

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