Chapter 1: Goods & Services Tax — Chapter Test | ML Aggarwal Solutions Understanding ICSE Mathematics Class 10

Chapter Test

Question 1

A shopkeeper bought a washing machine at a discount of 20% from a wholesaler, the printed price of the washing machine being ₹18000. The shopkeeper sells it to a consumer at a discount of 10% on the printed price. If the sales are intra-state and the rate of GST is 12%, find:

(i) the price inclusive of tax (under GST) at which the shopkeeper bought the machine.

(ii) the price which the consumer pays for the machine.

(iii) the tax (under GST) paid by the wholesaler to the State Government.

(iv) the tax (under GST) paid by the shopkeeper to the State Government.

(v) the tax (under GST) received by the Central Government.

Answer

It is a case of intra-state transaction of goods and services:

SGST = CGST = $\dfrac{1}{2} \times$ GST

Given:
Printed price of the washing machine = ₹18000
Rate of discount for shopkeeper = 20%
Cost Price of washing machine for shopkeeper = Printed Price - Discount

$= 18000 - \Big(\dfrac{20}{100} \times 18000 \Big) \\[0.5em] = 18000 - 3600 \\[0.5em] = ₹14400$

As the sales are intra-state and the rate of GST is 12%, so GST comprises of 6% as CGST and 6% as SGST. Wholesaler sells the washing machine to shopkeeper for ₹14400, amount of GST collected by wholesaler from shopkeeper (or paid by shopkeeper)

CGST = 6% of 14400 = $\dfrac{6}{100} \times$ 14400 = ₹864

SGST = 6% of 14400 = $\dfrac{6}{100} \times$ 14400 = ₹864

∴ Amount of Input GST of Shopkeeper:

Input CGST = ₹864
Input SGST = ₹864

Since the shopkeeper sells the article to consumer at a discount of 10% on printed price, the selling price of article by shopkeeper ( or cost price for consumer) = Printed Price - Discount

$= 18000 - \Big(\dfrac{10}{100}\times18000\Big) \\[0.5em] = 18000 - 1800 \\[0.5em] = ₹16200$

The amount of GST collected by shopkeeper (or paid by consumer):

CGST = 6% of 16200 = $\dfrac{6}{100} \times$ 16200 = ₹972

SGST = 6% of 16200 = $\dfrac{6}{100} \times$ 16200 = ₹972

∴ Amount of output GST of Shopkeeper:

Output CGST = 972
Output SGST = 972

(i) the price inclusive of tax (under GST) at which the shopkeeper bought the machine
= Cost price of washing machine for Shopkeeper + CGST paid by shopkeeper + SGST paid by shopkeeper
= 14400 + 864 + 864
= ₹16128

(ii) the price which the consumer pays for the machine
= Cost price of washing for consumer + CGST paid by consumer + SGST paid by consumer
= 16200 + 972 + 972
= ₹18144

(iii) the tax (under GST) paid by the wholesaler to the state Government.

Calculated above:

= ₹864.

(iv) the tax (under GST) paid by the shopkeeper to the State Government.
= Output SGST of Shopkeeper - Input SGST of Shopkeeper
= 972 - 864 = ₹108.

(v) the tax (under GST) received by the Central Government.
= CGST paid by Wholesaler + CGST paid by Shopkeeper
= 864 + 108 = ₹972.

Question 2

A manufacturer listed the price of his goods at ₹1600 per article. He allowed a discount of 25% to a wholesaler who in turn allowed a discount of 20% on the listed price to a retailer. The retailer sells one article to a consumer at a discount of 5% on the listed price. If all the sales are intra-state and the rate of GST is 5%, find:

(i) the price per article inclusive of tax (under GST) which the wholesaler pays.

(ii) the price per article inclusive of tax (under GST) which the retailer pays.

(iii) the amount which the consumer pays for the article.

(iv) the tax (under GST) paid by the wholesaler to the State Government for the article.

(v) the tax (under GST) paid by the retailer to the Central Government for the article.

(vi) the tax (under GST) received by the State Government.

Answer

It is a case of intra-state transaction of goods and services:

SGST = CGST = $\dfrac{1}{2} \times$ GST

Given:

Listed Price of article by manufacturer = ₹1600

Discount percentage given by manufacturer to wholesaler = 25%

Cost Price for wholesaler = Listed Price - Discount

$= 1600 - \Big(\dfrac{25}{100}\times1600\Big) \\[0.5em] = 1600 - 400 \\[0.5em] = ₹1200$

As the sales are intra-state and the rate of GST is 5%, so GST comprises of 2.5% as CGST and 2.5% as SGST. Manufacturer sells the article to wholesaler for ₹1200, amount of GST collected by manufacturer from wholesaler(or paid by wholesaler)

CGST = 2.5% of 1200 = $\dfrac{2.5}{100} \times$ 1200 = ₹30

SGST = 2.5% of 1200 = $\dfrac{2.5}{100} \times$ 1200 = ₹30

∴ Amount of Input GST of wholesaler:

Input CGST = ₹30
Input SGST = ₹30

Since the wholesaler sells the article to retailer at a discount of 20% on listed price, the selling price of article by wholesaler (or cost price for retailer) = Listed Price - Discount

$= 1600 - \Big(\dfrac{20}{100}\times 1600\Big) \\[0.5em] = 1600 - 320\\[0.5em] = ₹1280$

The amount of GST collected by wholesaler (or paid by retailer):

CGST = 2.5% of 1280 = $\dfrac{2.5}{100}\times$ 1280 = 32

SGST = 2.5% of 1280 = $\dfrac{2.5}{100}\times$ 1280 = 32

∴ Amount of output GST of wholesaler(or input GST of retailer):

Output CGST = 32
Output SGST = 32

Since the retailer sells the article to consumer at a discount of 5% on listed price, the selling price of article by retailer (or cost price for consumer) = Listed Price - Discount

$= 1600 - \Big(\dfrac{5}{100}\times1600\Big) \\[0.5em] = 1600 - 80 \\[0.5em] = ₹1520$

The amount of GST collected by retailer (or paid by consumer):

CGST = 2.5% of 1520 = $\dfrac{2.5}{100} \times$ 1520 = 38

SGST = 2.5% of 1520 = $\dfrac{2.5}{100} \times$ 1520 = 38

∴ Amount of output GST of retailer:

Output CGST = 38
Output SGST = 38

(i) the price per article inclusive of tax (under GST) which the wholesaler pays.
= Cost price of article for wholesaler + CGST paid by wholesaler + SGST paid by wholesaler
= 1200 + 30 + 30 = ₹1260

(ii) the price per article inclusive of tax (under GST) which the retailer pays.
= Cost price of article for retailer + CGST paid by retailer + SGST paid by retailer
= 1280 + 32 + 32 = ₹1344

(iii) the amount which the consumer pays for the article.
= Cost price of article for consumer + CGST paid by consumer + SGST paid by consumer
=1520 + 38 + 38 = ₹1596

(iv) the tax (under GST) paid by the wholesaler to the State Government for the article.
= Output SGST of wholesaler - Input SGST of wholesaler
= 32 - 30= ₹2

(v) the tax (under GST) paid by the retailer to the Central Government for the article.
= Output CGST of retailer - Input CGST of retailer
= 38 - 32= ₹6

(vi) the tax (under GST) received by the State Government.
= SGST paid by the manufacturer + SGST paid by the wholesaler + SGST paid by the retailer
= 30 + 2 + 6= ₹38

Question 3

John purchased a movie camera for ₹25488, which includes 10% rebate on the list price and 18% tax (under GST) on the remaining price. Find the marked price of the camera.

Answer

Given:

Rate of GST = 18%

Rebate (or discount) = 10% on Marked Price

Let the marked price be be P

Cost price of the article = Marked Price - Discount

$= \text{P} - 10% \text{ of P} \\[1em] = \text{P} - \Big(\dfrac{10}{100}\Big) \times \text{P} \\[1em] = \dfrac{100\text{P} - 10\text{P}}{100} \\[1em] = \dfrac{90\text{P}}{100} \\[1em] = 0.9\text{P}$

Amount of GST on cost price of article = 18% of 0.9P

Amount paid by John = Cost Price + GST = 25488

$\Rightarrow 0.9\text{P}+ \Big(\dfrac{18}{100}\times0.9\text{P}\Big) = 25488 \\[1em] \Rightarrow 0.9\text{P}+ 0.162\text{P} = 25488 \\[1em] \Rightarrow 1.062\text{P} = 25488 \\[1em] \Rightarrow \text{P} = \dfrac{25488}{1.062} = \bold{₹24000}$

Question 4

The marked price of an article is ₹7500. A shopkeeper buys the article from a wholesaler at some discount and sells it to a consumer at the marked price. The sales are intra-state and the rate of GST is 12%. If the shopkeeper pays ₹90 as tax (under GST) to the State Government, find:

(i) the amount of discount.

(ii) the price inclusive of tax (under GST) of the article which the shopkeeper paid to the wholesaler.

Answer

Given:

Marked Price of the article = ₹7500

Let discount rate be $x$ %

Cost price of article for shopkeeper = Marked Price - Discount

$= 7500 - \Big(\dfrac{x}{100}\times7500\Big) \\[1em] = ₹(7500 - 75x)$

As the sales are intra-state and the rate of GST is 12%, so GST comprises of 6% as CGST and 6% as SGST. wholesaler sells the article to shopkeeper for $7500 - 75x$ , amount of GST collected by wholesaler from shopkeeper(or paid by shopkeeper)

CGST = 6% of $(7500 - 75x) = \Big(\dfrac{6}{100}\Big)\times(7500 - 75x) = ₹(450 - 4.5x)$

SGST = 6% of $(7500 - 75x) = \Big(\dfrac{6}{100}\Big)\times(7500 - 75x) = ₹(450 - 4.5x)$

∴ Amount of Input GST of shopkeeper:

Input CGST = $₹(450 - 4.5x)$
Input SGST = $₹(450 - 4.5x)$

Cost Price for Consumer = Marked Price of the article (as given in question) = ₹7500

The amount of GST collected by shopkeeper (or paid by consumer):

CGST = 6% of 7500 = $\dfrac{6}{100}\times$ 7500 = ₹450

SGST = 6% of 7500 = $\dfrac{6}{100}\times$ 7500 = ₹450

∴ Amount of Output GST of shopkeeper:

Output CGST = ₹450
Output SGST = ₹450

As the shopkeeper pays a tax (under GST) of ₹90 to the State Government:

Tax paid to state government by shopkeeper = Output SGST of shopkeeper - Input SGST of shopkeeper = ₹90

$\Rightarrow 450 - (450 - 4.5x) = 90 \\[0.5em] \Rightarrow 4.5x = 90 \\[0.5em] \Rightarrow x = \dfrac{90}{4.5} = 20%$

(i) the amount of discount = Rate of discount x Marked Price

$= 20% \text{ of Marked Price} \\[1em] = \Big(\dfrac{20}{100}\Big) \times 7500 \\[1em] = \bold{₹1500}$

(ii) the price inclusive of tax (under GST) of the article which the shopkeeper paid to the wholesaler = Cost price of article for shopkeeper + CGST paid by shopkeeper + SGST paid by shopkeeper

$= (7500 - 75x) + (450 - 4.5x) + (450 - 4.5x) \\[1em] = (7500 - (75\times20)) + (450 - (4.5\times20)) + (450 - (4.5\times20)) \\[1em] = 6000 + 360 + 360 = \bold{₹6720}$

Question 5

A retailer buys an article at a discount of 15% on the printed price from a wholesaler. He marks up the price by 10% on the printed price but due to competition in the market, he allows a discount of 5% on the marked price to a buyer. If the rate of GST is 12% and the buyer pays ₹468.16 for the article inclusive of tax (under GST), find

(i) the printed price of the article.

(ii) the profit percentage of the retailer.

Answer

Given:

Rate of GST = 12%

Discount for retailer = 15% on Printed Price

Let the printed price be be P

Cost price of the article for retailer = Printed Price - Discount

$= \text{P} - 15% \text{ of P } \\[1em] = \text{P} - \Big(\dfrac{15}{100}\Big) \times \text{P} \\[1em] = \dfrac{100\text{P} - 15\text{P}}{100} \\[1em] = \dfrac{85\text{P}}{100} \\[1em] = 0.85\text{P} \\[1em]$

Amount of GST on cost price of article paid by retailer (or collected by the wholesaler)

$= 12% \text{ of } 0.85 \text{P} \\[1em] = \dfrac{12}{100}\times{0.85\text{P}} \\[1em] = 0.102\text{P}$

Since the retailer marks the price at 10% premium on printed price = Marked Price = Printed Price + Premium

$= \text{P} + 10% \text{ of P} \\[1em] = \text{P} + \Big(\dfrac{10}{100} \times P\Big) \\[1em] = \dfrac{\text{100P} + \text{10P}}{100} \\[1em] = \dfrac{110\text{P}}{100} \\[1em] = 1.1\text{P}$

Discount given by retailer on marked price to the buyer = 5%

$= 5% \text{ of Marked Price} \\[1em] = 5% \text{ of } 1.1\text{P} \\[1em] = \dfrac{5}{100}\times{1.1\text{P}} \\[1em] = \dfrac{5.5\text{P}}{100} \\[1em] = 0.055\text{P}$

Cost Price of the article for the buyer = Marked Price- Discount

$= 1.1\text{P} - 0.055\text{P} \\[1em] = 1.045\text{P}$

Amount of GST on cost price of article paid by buyer (or collected by the retailer)

$= 12% \text{ of } 1.045\text{P} \\[1em] = \dfrac{12}{100}\times{1.045\text{P}} \\[1em] = 0.1254\text{P}$

(i) The printed price of the article.

Amount paid by buyer for the article = Cost Price + GST = 468.16

$\Rightarrow 1.045\text{P} + 0.1254\text{P} = 468.16 \\[1em] \Rightarrow 1.1704\text{P} = 468.16 \\[1em] \Rightarrow \text{P} = \dfrac{468.16}{1.1704} = \bold{₹400}$

(ii) The profit percentage of the retailer.

Cost Price of the article for the buyer = 1.045P = 1.045 x 400 = ₹418

Cost Price of the article for the retailer = 0.85P = 0.85 x 400 = ₹340

Profit of the retailer = Selling Price of the article for the retailer (or cost price of buyer) - Cost price of the article for the retailer
= 418 - 340 = ₹78

Profit % of the retailer $= \dfrac{\text{Profit}}{\text{Cost}}\times{100} \\[1em] = \dfrac{78}{340}\times{100} \\[1em] = \dfrac{390}{17} \\[1em] = \bold{22\dfrac{16}{17}}%$

Question 6

Mrs. Arora bought the following articles from a departmental store :

S.No.	Item	Marked Price	Rate of GST	Discount
1	Hair oil	₹ 1200	18%	₹ 100
2	Cashew nuts	₹ 600	12%	-

Find the :

(a) Total GST paid.

(b) Total bill amount including GST.

Answer

(a) By formula,

GST on an article = (Price of item - Discount) × Rate of GST

GST on hair oil = (1200 - 100) × 18%

= 1100 × $\dfrac{18}{100}$

= 11 × 18

= ₹ 198.

GST on cashew nuts = (600 - 0) × 12%

= 600 × $\dfrac{12}{100}$

= 6 × 12

= ₹ 72.

Total GST paid = ₹ 198 + ₹ 72 = ₹ 270.

Hence, total GST paid = ₹ 270.

(b) Total bill amount including GST = Total cost price + Total GST paid

= [(₹ 1200 - ₹ 100) + ₹ 600] + ₹ 270

= ₹ 1100 + ₹ 600 + ₹ 270

= ₹ 1970.

Hence, total bill amount = ₹ 1970.

Question 7

The following bill shows the GST rate and the marked price of articles :

Vidhyut Electronics

S.No.	Item	Marked price	Quantity	Rate of GST
(a)	LED TV set	₹ 12,000	01	28%
(b)	MP4 player	₹ 5,000	01	18%

Find the total amount to be paid (including GST) for the above bill.

Answer

For LED TV set,

M.P. = ₹ 12,000

G.S.T. = 28%

G.S.T. amount = 28% of ₹ 12,000

= $\dfrac{28}{100} \times 12,000$

= 28 × 120

= ₹ 3360.

Total amount = ₹ 12,000 + ₹ 3360 = ₹ 15,360.

For MP4 player,

M.P. = ₹ 5,000

G.S.T. = 18%

G.S.T. amount = 18% of ₹ 5,000

= $\dfrac{18}{100} \times 5,000$

= 18 × 50

= ₹ 900.

Total amount = ₹ 5,000 + ₹ 900 = ₹ 5900.

Total bill = ₹ 15,360 + ₹ 5,900 = ₹ 21,260.

Hence, total bill = ₹ 21,260.

Question 8

The following bill shows the GST rate and the marked price of articles :

Rajdhani Departmental Store

S.No.	Item	Marked price	Discount	Rate of GST
(a)	Dry fruits (1 kg)	₹ 1200	₹ 100	12%
(b)	Packed Wheat Flour (5 kg)	₹ 286	Nil	5%
(c)	Bakery Products	₹ 500	10%	12%

Find the total amount to be paid (including GST) for the above bill.

Answer

For Dry fruits :

M.P. = ₹ 1200

Discount = ₹ 100

Discounted price = ₹ 1200 - ₹ 100 = ₹ 1100

GST = 12%

Tax = $\dfrac{12}{100} \times 1100$ = ₹ 132

Price including tax = ₹ 1100 + ₹ 132 = ₹ 1232.

For Wheat flour :

M.P. = ₹ 286

Discount = Nil

GST = 5%

Tax = $\dfrac{5}{100} \times 286$ = ₹ 14.30

Price including tax = ₹ 286 + ₹ 14.30 = 300.30

For bakery products :

M.P. = ₹ 500

Discount = 10% = $\dfrac{10}{100} \times 500$ = ₹ 50.

Discounted price = ₹ 500 - ₹ 50 = ₹ 450

GST = 12%

Tax = $\dfrac{12}{100} \times 450$ = ₹ 54

Price including tax = ₹ 450 + ₹ 54 = ₹ 504.

Total price = ₹ 1232 + ₹ 300.30 + ₹ 504 = ₹ 2036.30

Hence, total amount to be paid = ₹ 2036.30

Chapter 1

Goods & Services Tax — Chapter Test

Class - 10 ML Aggarwal Understanding ICSE Mathematics

Chapter Test

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8