Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1C

Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1C

These Solutions are part of Selina Concise Mathematics Class 10 ICSE Solutions. Here we have given Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1C.

Other Exercises

[In this exercise, all the prices are excluding tax/VAT unless specified].
Question 1.
Madan purchases a compact computer system for ₹ 47,700 which includes 10% rebate on the marked price and then 6% Sales Tax on the remaining price. Find the marked price of the computer.
Solution:
Sales price of the computer = ₹ 47700
Rate of Sales Tax = 6%
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1C 1.1
Hence marked price = ₹ 50,000

Question 2.
An article is marked at ₹ 500. The wholesaler sells it to a retailer at 20% discount and charges sales-tax on the remaining price at 12.5%. The retailer, in turn, sells the article to a customer at its marked price and charges sales-tax at the same rate. Calculate :
(i) the price paid by the customer.
(ii) the amount of VAT paid by the retailer.
Solution:
Marked price of an article = ₹ 500
Rate of discount = 20%
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1C 2.1
(i) Price paid by-the customer = ₹ 500 + ₹ 62.50 = ₹ 562.50
(ii) VAt paid by the retailer = ₹ 62.50 – ₹ 50.00 = ₹ 12.50

Question 3.
An article is marked at ₹ 4,500 and the rate of sales-tax on it is 6%. A trader buys this article at some discount and sells it to a customer at the marked price. If the trader pays ₹ 81 as VAT; find :
(i) how much per cent discount does the trader get ?
(ii) the total money paid by the trader, including tax, to buy the article.
Solution:
Marked price = ₹ 4500
Rate of S.T. = 6%
VAT paid by the trader = ₹ 81
C.P. for the customer = ₹ 4500
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1C 3.1

Question 4.
A retailer sells an article for ₹ 5,350 including 7% Sales Tax on the listed price. If he had bought it at a discount and has made a profit of 25% on the whole, And the rate of discount he gets.
Solution:
S.P. of an article of the retailer (including S.T.) = ₹ 5350
Rate of S.T. = 7%
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1C 4.1

Question 5.
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 tax at the same rate. Find :
(i) The price at which the camera can be bought from the shopkeeper.
(ii) The VAT (Value Added Tax) paid by the shopkeeper. (2008)
Solution:
Printed price (M.P) = ₹ 1600
Rate of discount = 20%
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1C 5.1
(i) The buyers bought the camera = ₹ 1600 + ₹ 96 = ₹ 1696
(ii) VAT paid by the shopkeeper = ₹ 96 – ₹ 76.80 = ₹ 19.20

Question 6.
Tarun bought an article for ₹ 8000 and spent ₹ 1000 for transportation. He marked the article at ₹ 11,700 and sold it to a customer. If the customer had to pay 10% sales tax, find:
(i) The customer’s price
(ii) Tarun’s profit percent.
Solution:
Tarun’s cost price = ? 8000
Transportation charges = ₹ 1000
Tarun’s total cost = (₹ 8000 + ₹ 1000) = ₹ 9000
Tarun’s selling price = ₹ 11,700
Rate of sales tax = 10%
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1C 6.1

Question 7.
A shopkeeper sells an article at the listed price of ₹ 1,500 and the rate of VAT is 12% at each stage of sale. If the shopkeeper pays a VAT of ₹ 36 to the Government, what was the price, inclusive of Tax, at which the shopkeeper purchased the articles from the wholesaler?
Solution:
Tax charged by shopkeeper
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1C 7.1

Question 8.
A shopkeeper bought a washing machine at a discount of 20% from a wholesaler, the printed price of the washing machine being ₹ 18,000. The shopkeeper sells it to a consumer at a discount of 10% on the printed price. If the rate of sales tax under is 8%, find:
(i) the VAT paid by the shopkeeper.
(ii) the total amount that the consumer pays for the washing machine. (2014)
Solution:
(i) S.P. of washing machine
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1C 8.1
VAT paid by shopkeeper = Tax charged – Tax paid = ₹ 1296 – ₹ 1152 = ₹144
(ii) Price paid by customer = ₹ 16200 + ₹ 1296 = ₹ 17496

Question 9.
Mohit, a dealer in electronic goods, buys a high class TV set for ₹ 61,200. He sells this TV set to Geeta, Geeta to Rohan and Rohan sells it to Manoj. If the profit at each stage is ₹ 2,000 and the rate of VAT at each stage is 12.5%, find :
(i) total amount of tax (under VAT) paid to the Government.
(ii) Money paid by Manoj to buy the TV set.
Solution:
For Mohit,
C.P. of electronic goods = ₹ 61200
Amount of profit in each case = ₹ 2000
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1C 9.1
Net VAT = ₹ 8400 – ₹ 8150 = ₹ 250
(i) Total amount of VAT paid to govt. = ₹ 7650 + ₹ 250 + ₹ 250 + ₹ 250 = ₹ 8400
(ii) Money paid by Manoj to buy the T.V. set = ₹ 67200 + ₹ 8400 = ₹ 75600

Question 10.
A shopkeeper buys an article at a discount of 30% of the list price which is ₹ 48,000. In turn, the shopkeeper sells the article at 10% discount. If the rate of VAT is 10%, find the VAT to be paid by the shopkeeper.
Solution:
Market value (M.P.) of an article = ₹ 48000
Rate of discount = 30%
Amount of discount = ₹ 48000 x \(\frac { 30 }{ 100 }\) = ₹ 14400
(i) Cost price of shopkeeper = ₹ 48000 – ₹ 14400 = ₹ 33600
(ii) C.P. for shopkeeper = ₹ 33600
Rate of VAT = 10%
Amount of VAT paid by shopkeeper
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1C 10.1
Net VAT paid by the shopkeeper = VAT recovered from customer – VAT paid to dealer
= ₹ 4320 – ₹ 3360 = ₹ 960

Question 11.
A company sells an article to a dealer for ₹ 40,500 including VAT (sales-tax). The dealer sells it to some other dealer for ₹ 42,500 plus tax. The second dealer sells it to a customer at a profit of ₹ 3,000. If the rate of sales-tax under VAT is 8%, find :
(i) the cost of the article (excluding tax) to the first dealer.
(ii) the total tax (under VAT) received by the Government.
(iii) the amount that a customer pays for the article.
Solution:
For a company,
S.P. of an article including VAT = ₹ 40500
Rate of VAT = 8%
(i) Amount of article excluding VAT
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1C 11.1
= ₹ 425 x 108 = ₹ 45900
Total tax (VAT) = ₹ 45900 – ₹ 42500 = ₹ 3000
S.P. for the second dealer = ₹ 42500 + ₹ 3000 = ₹ 45500
(ii) VAT = ₹ \(\frac { 45500 x 8 }{ 100 }\) = ₹ 3640
(iii) Total amount paid by customer = ₹ 45500 + ₹ 3640 = ₹ 49140

Question 12.
A wholesaler buys a TV from the manufacturer for ₹ 25,000. He marks the price of the TV 20% above his cost price and sells it to a retailer at 10% discount on the marked price. If the rate of VAT is 8%, find the :
(i) marked price.
(ii) retailer’s cost price inclusive of tax.
(iii) VAT paid by the wholesaler. (2015)
Solution:
S.P. for the manufactures = ₹ 25000
or C.P. for a whole seller a T.V. = ₹ 25000
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1C 12.1
C.P. for the retailer = ₹ 27000 + ₹ 2160 = ₹ 29160
(iii) VAT paid by the whole seller = ₹ 2160 – ₹ 2000 = ₹ 160

Question 13.
A dealer buys an article at a discount of 30 % from the wholesaler, the marked price being ₹ 6,000. The dealer sells it to a shopkeeper at a discount of 10% on the marked price. If the rate of VAT is 6%, find :
(i) the price paid by the shopkeeper including the tax.
(ii) the VAT paid by the dealer. (2016)
Solution:
Market price of the article = ₹ 6000
A dealer buys an article at a discount of 30% from the wholesaler.
Price of the article which the dealer paid to the wholesaler = 6000 – 30% of 6000
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1C 13.1
Amount of the article inclusive of sales tax at which the dealer bought it
= ₹ 4200 + ₹ 252 = ₹ 4452
Dealer sells the article at a discount of 10% to the shopkeeper.
Price of the article which the shopkeeper paid to the dealer = ₹ 6000 – 10% of 6000
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1C 13.2
Amount of the article inclusive of sales tax at which the shopkeeper bought it
= ₹ 5400 + ₹ 324 = ₹ 5724
The value added by dealer = ₹ 5400 – ₹ 4200 = ₹ 1200
Amount of VAT paid by dealer = 6% of 1200
= \(\frac { 6 }{ 100 }\) x 1200 = ₹ 72
Price paid by shopkeeper including tax is ₹ 5724
VAT paid by dealer is ₹ 72

Hope given Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1C are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1B

Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1B

 

These Solutions are part of Selina Concise Mathematics Class 10 ICSE Solutions. Here we have given Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1B.

Other Exercises

[In this exercise, all the prices are excluding tax/VAT unless specified].
Question 1.
A shopkeeper purchases an article for ₹ 6,200 and sells it to a customer for ₹ 8,500. If the sale tax (under VAT) is 8%; find the VAT paid by the shopkeeper.
Solution:
C.P. of article = ₹ 6200
Rate of VAT = 8%
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1B 1.1
Amount of VAT paid by the shopkeeper = ₹ 680 – ₹ 496 = ₹ 184

Question 2.
A purchases an article for ₹ 3,600 and sells it to B for ₹ 4,800. B, in turn, sells the article to C for ₹ 5,500. If the sale tax (under VAT) is 10%, find the VAT levied on A and B.
Solution:
C.P. of an article for A = ₹ 3600
C.P. of the article for B = ₹ 4800
and C.P. for C = ₹ 5500
Rate of VAT in each case = 10%
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1B 2.1
Now VAT levied on A = ₹ 480 – ₹ 360 = ₹ 120
and VAT levied on B = ₹ 550 – ₹ 480 = ₹ 70

Question 3.
A manufacturer buys raw material for ₹ 60,000 and pays 4% tax. He sells the ready stock for ₹ 92,000 and charges 12.5% tax. Find the VAT paid by the manufacturer.
Solution:
C.P. of raw material = ₹ 60000
Rate of tax = 4%
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1B 3.1
VAT paid by the manufacturer = ₹ 11500 – ₹ 2400 = ₹ 9100

Question 4.
The cost of an article is ₹ 6,000 to a distributor. He sells it to a trader for ₹ 7,500 and the trader sells it to a customer for ₹ 8,000. If the VAT rate is 12.5% ; find the VAT paid by the :
(i) distributor
(ii) trader.
Solution:
Cost price of an article to a distributor = ₹ 6000
and selling price of distributor = ₹ 7500
and selling price of trader = ₹ 8000
Rate of VAT = 12.5% = \(\frac { 25 }{ 2 }\) %
Now, VAT for two distributor
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1B 4.1
(i) Now VAT paid by distributor = ₹ 937.50 – ₹ 750 = ₹ 187.50
(ii) and VAT paid by trader = ₹ 1000 – ₹ 937.50 = ₹ 62.50

Question 5.
The printed price of an article is ₹ 2,500. A wholesaler sells it to a retailer at 20% discount and charges sales-tax at the rate of 10%. Now the retailer, in turn, sells the article to a customer at its list price and charges the sales-tax at the same rate. Find :
(i) the amount that retailer pays to the wholesaler.
(ii) the VAT paid by the retailer.
Solution:
M.P. of an article = ₹ 2500
Rebate = 20%
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1B 5.1

Question 6.
A retailer buys an article for ₹ 800 and pays the sales-tax at the rate of 8%. The retailer sells the same article to a customer for ₹ 1,000 and charges sales- tax at the same rate. Find :
(i) the price paid by a customer to buy this article.
(ii) the amount of VAT paid by the retailer.
Solution:
C.P. of an article for retailer = ₹ 800
Rate of S.T. = 8%
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1B 6.1
(i) Cost price of the customer = ₹ 1000 + ₹ 80 = ₹ 1080
(ii) VAT paid by the retailer = ₹ 80 – ₹ 64 = ₹ 16

Question 7.
A shopkeeper buys 15 identical articles for ₹ 840 and pays sales-tax at the rate of 8%. He sells 6 of these articles at ₹ 65 each and charges sales-tax at the same rate. Calculate the VAT paid by the shopkeeper against the sale of these six articles.
Solution:
C.P. of 15 articles = ₹ 840
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1B 7.1
VAT paid by the retailer = ₹ 31.20 – ₹ 26.88 = ₹ 4.32

Question 8.
The marked price of an article is ₹ 900 and the rate of sales-tax on it is 6%. If on selling the article at its marked price, a retailer has to pay VAT = ₹ 4.80; find the money paid by him (including sales-tax) for purchasing this article.
Solution:
M.P. an article = ₹ 900
Rate of S.T. = 6%
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1B 8.1
Amount paid including S.T. = ₹ 820 + ₹ 49.20 = ₹ 869.20

Question 9.
A manufacturer marks an article at ₹ 5,000. He sells this article 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 its marked price. If the retailer sells the article without any discount and at each stage the sales-tax is 8%, calculate the amount of VAT paid by :
(i) the wholesaler.
(ii) the retailer.
Solution:
M.P. of an article = ₹ 5000
Rate of discount = 25%
S.R of the manufacturer or C.P of
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1B 9.1
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1B 9.2
Now VAT paid by
(i) The wholesaler = ₹ 340 – ₹ 300 = ₹ 40
(ii) Retailer = ₹ 400 – ₹ 340 = ₹ 60

Question 10.
A shopkeeper buys an article at a discount of 30% and pays sales-tax at the rate of 8%. The shopkeeper, in turn, sells the article to a customer at the printed price and charges sales tax at the same rate. If the printed price of the article is ₹ 2,500; find :
(i) the price paid by the shopkeeper.
(ii) the price paid by the customer.
(iii) The VAT (Value Added Tax) paid by the shopkeeper.
Solution:
Printed price of an article = ₹ 2500
Discount = 30%
C.P of the article for shopkeeper
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1B 10.1
(i) Price paid by the shopkeeper = ₹ 1750 + ₹ 140 = ₹ 1890
(ii) Price paid by the customer = ₹ 2500 + ₹ 200 = ₹ 2700
(iii) VAT paid by the shopkeeper = ₹ 200 – ₹ 140 = ₹ 60

Question 11.
A shopkeeper sells an article at its list price (₹ 3,000) and charges sales-tax at the rate of 12%. If the VAT paid by the shopkeeper is ₹ 72, at what price did the shopkeeper buy the article inclusive of sales-tax ?
Solution:
S.P. or list price of an article = ₹ 3000
Rate of sales tax = 12%
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1B 11.1
C.P paid by the shopkeeper including S.T. = ₹ 2400 + ₹ 288 = ₹ 2688

Question 12.
A manufacturer marks an article for ₹ 10,000. He sells it to a wholesaler at 40% discount. The wholesaler sells this article to a retailer at 20% discount on the marked price of the article. If retailer sells the article to a customer at 10% discount and the rate of sales-tax is 12% at each stage; find the amount of VAT paid by the :
(i) wholesaler
(ii) retailer
Solution:
Marked price of an article = ₹ 10000
Rate of discount = 40%
C.P of the wholesaler
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1B 12.1
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1B 12.2
Now
(i) Vat paid by wholesaler = ₹ 960 – ₹ 720 = ₹ 240
(ii) Vat paid by retailer = ₹ 1080 – ₹ 960 = ₹ 120

Hope given Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1B are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1A

Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1A

These Solutions are part of Selina Concise Mathematics Class 10 ICSE Solutions. Here we have given Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1A.

Other Exercises

Question 1.
Rajat purchases a wrist-watch costing ₹ 540. The rate of Sales Tax is 8%. Find the total amount paid by Rajat for the watch.
Solution:
Cost of watch = ₹ 540
Rate of Sales Tax = 8%
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1A 1.1
Total Amount of Watch = ₹ 540 + ₹ 43.20 = ₹ 583.20

Question 2.
Ramesh paid ₹ 345.60 as Sales Tax on a purchase of ₹ 3,840. Find the rate of Sales Tax.
Solution:
On ₹ 3840, sales-tax is = ₹ 345.60
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1A 2.1

Question 3.
The price of a washing machine, inclusive of sales tax is ₹ 13,530/-. If the Sales Tax is 10%, find its basic (cost) price. [2003]
Solution:
Selling price of washing machine = ₹ 13,530.
Rate of Sales Tax = 10%
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1A 3.1

Question 4.
Sarita purchases biscuits costing ₹ 158 on which the rate of Sales Tax is 6%. She also purchases some cosmetic goods costing ₹ 354 on which the rate of Sales Tax is 9%. Find the total amount to be paid by Sarita.
Solution:
Cost of biscuits = ₹ 158.
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1A 4.1
Total cost of cosmetic goods = ₹ 354 + ₹ 31.86 = ₹ 385.86
Total amount paid by Sarita = ₹ 167. 48 + ₹ 385.86 = ₹ 553. 34

Question 5.
The marked price of two articles A and B together is ₹ 6,000. The sales tax on article A is 8% and that on article B is 10%. If on selling both the articles, the total sales tax collected is ₹ 552, find the marked price of each of the articles A and B.
Solution:
M.P of two articles A and B = ₹ 6000
Rate of S.T. on A = 8%
and rate of S.I. on B = 10%
Total sales tax on A and B = ₹ 552
Let MP of A be = ₹ x
and then of MP of B = ₹ (6000 – x)
according to the condition,
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1A 5.1
M.P. of article A = ₹ 2400
and MP of article B = ₹ 6000 – ₹ 2400 = ₹ 3600

Question 6.
The price of a T.V. set inclusive of sales tax of 9% is ₹ 13,407. Find its marked price. If Sales Tax is increased to 13%, how much more does the customer has to pay for the T.V. ? [2002]
Solution:
Sale price of T.V. set = ₹ 13,407
Rate of sales tax = 9%
Let marked price of T.V. = x
Then sale price
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1A 6.1
Sale price = ₹ 12,300 + ₹ 1,599 = ₹ 13,899
Difference between the two sales price = ₹ 13,899 – ₹ 13,407 = ₹ 492

Question 7.
The price of an article is ₹ 8,250 which includes Sales Tax at 10%. Find how much more or less does a customer pay for the article, if the Sales Tax on the article:
(i) increases to 15%
(ii) decreases to 6%
(iii) increases by 2%
(iv) decreases by 3%
Solution:
Price of an article = ₹ 8,250
Rate of Sales Tax = 10%
Let the list price = x
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1A 7.1
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1A 7.2
The customer will have to pay less = ₹ 8,250 – ₹ 8,025 = ₹ 225

Question 8.
A bicycle is available for ₹ 1,664 including Sales Tax. If the list price of the bicycle is ₹ 1,600, find :
(i) the rate of Sales Tax
(ii) the price a customer will pay for the bicycle if the Sales Tax is increased by 6%.
Solution:
Sale price of bicycle = ₹ 1,664.
List price = ₹ 1,600
Amount of Sales Tax = ₹ 1,664 – ₹ 1,600 = ₹ 64.
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1A 8.1
Sales price = ₹ 1,600 + ₹ 160 = ₹ 1,760

Question 9.
When the rate of sale-tax is decreased from 9% to 6% for a coloured T.V.; Mrs Geeta will save ₹ 780 in buying this T.V. Find the list price of the T.V.
Solution:
Rate of sales tax in the beginning = 9%
and Reduced rate = 6%
Diff. = 9 – 6 = 3%
Total saving = ₹ 780
List, price of TV = Total saving x \(\frac { 100 }{ 3 }\)
= \(\frac { 780 x 100 }{ 3 }\) = ₹ 26000

Question 10.
A trader buys an unfinished article for ₹ 1,800 and spends ₹ 600 on its finishing, packing, transportation, etc. He marks the article at such a price that will give him 20% profit. How much will a customer pay for the article including 12% sales tax.
Solution:
Cost price of an unfinished article = ₹ 1800
Cost on finishing, packing etc or over head charges = ₹ 600
Total C.P. = ₹ 1800 + ₹ 600 = ₹ 2400
Gain = 20%
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1A 10.1
Total sale price = ₹ 2880 + ₹ 345.60 = ₹ 3225.60

Question 11.
A shopkeeper buys an article for ₹ 800 and spends ₹ 100 on its transportation, etc. He marks the article at a certain price and then sells it Tor ₹ 1,287 including 10% sales tax. Find this profit as per cent.
Solution:
C.P. of an article = ₹ 800
Over head charges = ₹ 100
Total C.P. = ₹ 800 + ₹ 100 = ₹ 900
Sale price = ₹ 1287 including S.T.
Rate of S.T. = 10%
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1A 11.1

Question 12.
A shopkeeper announces a discount of 15% on his goods. If the marked price of an article, in his shop, is ₹ 6000 ; how much a customer has to pay for it, if the rate of Sales Tax is 10% ?
Solution:
Marked price of an article = ₹ 6000
Rate of discount = 15%
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1A 12.1

Question 13.
The catalogue price of a music system is ₹ 24,000. The shopkeeper gives a discount of 8% on the list price. He gives a further off-season discount of 5% on the balance. But Sales Tax at 10% is charged on the remaining amount. Find:
(a) the Sales Tax a customer has to pay.
(b) the final price he has to pay for the music system. (2001)
Solution:
List price of colour music system = ₹ 24,000
First rate of discount = 8%
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1A 13.1
(b) Final price of music system = ₹ 20,976 + ₹ 2,097.60 = ₹ 23,073.60

Hope given Selina Concise Mathematics Class 10 ICSE Solutions Chapter 1 Value Added Tax Ex 1A are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

Selina Concise Mathematics Class 10 ICSE Solutions Chapter 6 Solving Problems Ex 6A

Selina Concise Mathematics Class 10 ICSE Solutions Chapter 6 Solving Problems (Based on Quadratic Equations) Ex 6A

These Solutions are part of Selina Concise Mathematics Class 10 ICSE Solutions. Here we have given Selina Concise Mathematics Class 10 ICSE Solutions Chapter 6 Solving Problems Ex 6A.

Other Exercises

Question 1.
The product of two consecutive integers is 56. Find the integers.
Solution:
Let the first integer = x
Then second integer = x + 1
Now according to the condition given
x (x + 1) = 56
⇒ x² + x – 56 = 0
⇒ x² + 8x – 7x – 56 = 0
⇒ x (x + 8) – 7 (x + 8) = 0
⇒ (x + 8) (x – 7) = 0
Either x + 8 = 0, then x = – 8
or x – 7 = 0, then x = 7
(i) If x = -8, then
first integer = -8
and second integer = – 8 + 1 = – 7
(ii) If x = 7, then
first integer = 7
and second integer = 7 + 1 = 8
Integers are 7, 8 or -8, -7

Question 2.
The sum of the squares of two consecutive natural numbers is 41. Find the numbers.
Solution:
Let the first natural number = x
Then second natural number = x + 1
Now according to the condition given,
(x)² + (x + 1)² = 41
⇒ x² + x² + 2x + 1 = 41
⇒ 2x² + 2x + 1 – 41 = 0
⇒ 2x² + 2x – 40 = 0
⇒ x² + x – 20 = 0 (Dividing by 2)
⇒ x² + 5x – 4x – 20 = 0
⇒ x (x + 5) – 4 (x + 5) = 0
⇒ (x + 5) (x – 4) = 0
Either x + 5 = 0 then x = – 5 But it is not a natural number
or x – 4 = 0, Then x = 4
Numbers are 4 and 5

Question 3.
Find the two natural numbers which differ by 5 and the sum of whose squares is 97.
Solution:
Let the first natural number = x
Then second natural number = x + 5
Now according to the given condition,
(x)² + (x + 5)² = 97
⇒ x² + x² + 10x + 25 – 97 = 0
⇒ 2x² + 10x – 72 = 0
⇒ x² + 5x – 36 = 0 (Dividing by 2)
⇒ x² + 9x – 4x – 36 = 0
⇒ x (x + 9) – 4 (x + 9) = 0
⇒ (x + 9) (x – 4) = 0
Either x + 9 = 0, then x = – 9 But it is not a natural number
or x – 4 = 0, then x = 4
First number = 4
and second number = 4 + 5 = 9

Question 4.
The sum of a number and its reciprocal is 4.25. Find the number.
Solution:
Let the number = x
Now according to the condition,
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 6 Solving Problems Ex 6A Q4.1
⇒ 4x (x – 4) – 1 (x – 4) = 0
⇒ (x – 4) (4x – 1) = 0
Either x – 4 = 0, then x = 4
or 4x – 1 = 0, 4x = 1 then x = \(\frac { 1 }{ 4 }\)
Number is 4 or \(\frac { 1 }{ 4 }\)

Question 5.
Two natural numbers differ by 3. Find the numbers, if the sum of their reciprocals is \(\frac { 7 }{ 10 }\)
Solution:
Let the first natural number = x
Then second natural number = x + 3
Now according to the given condition,
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 6 Solving Problems Ex 6A Q5.1
But it is not a natural number
or x – 2 = 0, then x = 2
First number = 2
and second number = 2 + 3 = 5

Question 6.
Divide 15 into two parts such that the sum of their reciprocals is \(\frac { 3 }{ 10 }\).
Solution:
Let first part = x
Then second part = 15 – x (sum = 15)
Now according to the given condition,
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 6 Solving Problems Ex 6A Q6.1
⇒ x (x – 5) – 10 (x – 5) = 0
⇒ (x – 5) (x – 10) = 0
Either x – 5 = 0, then x = 5
or x – 10 = 0, then x = 10
If x = 5, then first part = 15 – 5 = 10
If x = 10, then second part = 15 – 10 = 5
Parts are 5, 10

Question 7.
The sum of the squares of two positive integers is 208. If the square of the larger number is 18 times the smaller number, find the numbers.
Solution:
Let x be the larger number and y be the smaller number, then
According to the conditions x2 = 18 ….(i)
and x² + y² = 208 ….(ii)
⇒ 18y + y² = 208 [From (i)]
⇒ y² + 18y – 208 = 0
⇒ y² + 26y – 8y – 208 = 0
⇒ y (y + 26) – 8 (y + 26) = 0
⇒ (y + 26) (y – 8) = 0
Either y + 26 = 0, then y = -26
But it is not possible as it is not positive
or y – 8 = 0, then y = 8
Then x² = 18y ⇒ y² = 18 x 8 ⇒x² = 144 = (12)² ⇒ x = 12
Number are 12, 8

Question 8.
The sum of the squares of two consecutive positive even numbers is 52. Find the numbers.
Solution:
Let first even number = 2x
and second even number = 2x + 2
Now according to the given condition,
(2x)² + (2x + 2)² = 52
⇒ 4x² + 4x² + 8x + 4 = 52
⇒ 4x² + 4x² + 8x + 4 – 52 = 0
⇒ 8x² + 8x – 48 = 0
⇒ x² + x – 6 = 0 (Dividing by 8)
⇒ x² + 3x – 2x – 6 = 0
⇒ x (x + 3) – 2 (x + 3) = 0
⇒ (x + 3) (x – 2) = 0
Either x + 3 = 0, then x = – 3 But it is not possible because it is not positive.
or x – 2 = 0, then x = 2
First even number = 2 x 2 = 4
Second number = 4 + 2 = 6
Hence numbers are 4, 6

Question 9.
Find two consecutive positive odd numbers, the sum of whose squares is 74.
Solution:
Let first odd number = 2x -1
Second odd number = 2x – 1 + 2 = 2x + 1
Now according to the given condition,
(2x – 1)² + (2x + 1)² = 74
⇒ 4x² – 4x + 1 + 4x² + 4x + 1 = 74
⇒ 8x² + 2 – 74 = 0
⇒ 8x² – 72 = 0
⇒ x² – 9 = 0 (Dividing by 8)
⇒ (x + 3) (x – 3) = 0
Either x + 3 = 0, then x = -3 But it is not possible because it is not positive.
or x – 3 = 0, then x = 3
First odd number = 2x – 1 = 2 x 3 – 1 = 6 – 1 = 5
and second odd number = 5 + 2 = 7
Number are 5, 7

Question 10.
The denominator of a positive fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is 2.9; find the fraction.
Solution:
Let numerator of a fraction = x
Then denominator = 2x + 1
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 6 Solving Problems Ex 6A Q10.1
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 6 Solving Problems Ex 6A Q10.2

Question 11.
Three positive numbers are in the ratio \(\frac { 1 }{ 2 }\) : \(\frac { 1 }{ 3 }\) : \(\frac { 1 }{ 4 }\) Find the numbers; if the sum of their squares is 244.
Solution:
Multiply each ratio by L.C.M. of de-nominators i.e. by 12.
We get, 6 : 4 : 3
Let first positive number = 6x
Then second number = 4x
and third number = 3x
According to the given condition,
(6x)² + (4x)² + (3x)² = 244
⇒ 36x² + 16x² + 9x² = 244
⇒ 61x² = 244
⇒ x² – 4 = 0
⇒ (x + 2) (x – 2) = 0
Either x + 2 = 0, then x = -2 But it is not possible because it is not positive
or x – 2 = 0, then x = 2
First number = 6x = 6 x 2 = 12
Second number = 4x = 4 x 2 = 8
and third number = 3x = 3 x 2 = 6
Numbers are 12, 8, 6

Question 12.
Divide 20 into two parts such that three times the square of one part exceeds the other part by 10.
Solution:
Let first part = x
Then second part = 20 – x (Sum = 20)
Now, according to the given condition,
3(x)² – (20 – x) = 10
⇒ 3x² – 20 + x – 10 = 0
⇒ 3x² + x – 30 = 0
⇒ 3x² + 10x – 9x – 30 = 0
⇒ x (3x + 10) – 3 (3x + 10) = 0
⇒ (3x + 10) (x – 3) = 0
Either 3x + 10 = 0, then 3x = -10 ⇒ x = \(\frac { -10 }{ 3 }\)
But it is not possible.
or x – 3 = 0 then x = 3
Then first part = 3
and second part = 20 – 3 = 17

Question 13.
Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 60. Assume the middle number to be x and form a quadratic equation satisfying the above statement Hence ; find the three numbers.
Solution:
Let middle number = x
Then, first number = x – 1
and third number = x + 1
Now according to the condition,
(x)²= [(x + 1)² – (x – 1)²] + 60
⇒ x² = [x² + 2x + 1 – x² + 2x – 1 ] + 60
⇒ x² = 4x + 60
⇒ x² – 4x – 60 = 0
⇒ x² – 10x + 6x – 60 = 0
⇒ x (x – 10) + 6 (x – 10) = 0
⇒ (x – 10) (x + 6) = 0
Either x – 10 = 0 then x = 10
or x + 6 = 0 then x = -6. But it is not a natural number.
Middle number = 10
First number = 10 – 1 = 9
and third number = 10 + 1 = 11
Hence numbers are 9, 10, 11

Question 14.
Out of three consecutive positive integers, the middle number is p. If three times the square of the largest is greater than the sum of the squares of the other two numbers by 67; calculate the value of p.
Solution:
Middle number = p
then smallest number = p – 1
and greatest number = p + 1
Now, according to the condition.
3 (p + 1)² – (p – 1)² – p² = 67
⇒ 3 (p² + 2p + 1) – (p² – 2p + 1) – p² = 67
⇒ 3p² + 6p + 3 – p² + 2p – 1 – p² – 67 = 0
⇒ p² + 8p + 2 – 67 = 0
⇒ p² + 8p – 65 = 0
⇒ p² + 13p – 5p – 65 = 0
⇒ p (p + 13) – 5 (p + 13) = 0
⇒ (p + 13) (p – 5) = 0
Either p + 13 = 0, then p = -13 But it is not possible.
or p – 5 = 0, then p = 5
p = 5

Question 15.
A can do a piece of work in ‘x’ days and B can do the same work in (x + 16) days. If both working together can do it in 15 days. Calculate ‘x’.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 6 Solving Problems Ex 6A Q15.1
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 6 Solving Problems Ex 6A Q15.2

Question 16.
One pipe can fill a cistern in 3 hours less than the other. The two pipes together can fill the cistern in 6 hours 40 minutes. Find the time that each pipe will take to fill the cistern.
Solution:
Let first pipe can fill the cistern in = x hrs.
Second pipe will fill the cistern in = x – 3 hrs.
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 6 Solving Problems Ex 6A Q16.1
But it is not possible.
x = 15
First pipe can fill in 15 hrs.
and second pipe in 15 – 3 = 12 hrs.

Question 17.
A positive number is divided into two parts such that the sum of the squares of the two parts is 20. The square of the larger part is 8 times the smaller part. Taking A as the smaller part of the two parts. Find the number. (2010)
Solution:
Let larger part = y
and smaller part = x
x² + y² = 20 ….(i)
and y² = 8x ….(ii)
Substituting the value of y² in „
x² + 8x = 20
⇒ x² + 8x – 20 = 0
⇒ x² + 10x – 1x – 20 = 0 {-20 = 10 x (-2), 8 = 10 – 2}
⇒ x (x + 10) – 2(x + 10) = 0
⇒ (x + 10) (x – 2) = 0
Either x + 10 = 0, then x = – 10 which is not possible because it is negative
or x – 2 = 0, then x = 2
Smaller number = 2
and larger number = y² = 8x = 8 x 2 = 16
⇒ y² = 16 = (4)²
⇒ y = 4
Number = x + y = 2 + 4 = 6

Hope given Selina Concise Mathematics Class 10 ICSE Solutions Chapter 6 Solving Problems Ex 6A are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.

Selina Concise Mathematics Class 10 ICSE Solutions Chapter 24 Measures of Central Tendency Ex 24A

Selina Concise Mathematics Class 10 ICSE Solutions Chapter 24 Measures of Central Tendency (Mean, Median, Quartiles and Mode) Ex 24A

These Solutions are part of Selina Concise Mathematics Class 10 ICSE Solutions. Here we have given Chapter 24 Measures of Central Tendency (Mean, Median, Quartiles and Mode) Ex 24A.

Other Exercises

Question 1.
Find the mean of following set of numbers:
(i) 6, 9, 11, 12 and 7
(ii) 11, 14, 23, 26, 10, 12, 18 and 6.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 24 Measures of Central Tendency Ex 24A Q1.1

Question 2.
Marks obtained (in mathematics) by a students are given below :
60, 67, 52, 76, 50, 51, 74, 45 and 56
(a) Find the arithmetic mean
(b) If marks of each student be increased by 4;
what will be the new value of arithmetic mean.
Solution:
(a) Hence x = 9
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 24 Measures of Central Tendency Ex 24A Q2.1
(b) If marks of each students be increased by 4 then new mean will be = 59 + 4 = 63

Question 3.
Find the mean of natural numbers from 3 to 12.
Solution:
Numbers betweeen 3 to 12 are 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.
Here n = 10
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 24 Measures of Central Tendency Ex 24A Q3.1

Question 4.
(a) Find the means of 7, 11, 6, 5 and 6. (b) If each number given in (a) is diminished by 2; find the new value of mean.
Solution:
(a) The mean of 7, 11, 6, 5 and 6.
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 24 Measures of Central Tendency Ex 24A Q4.1
(b) If we subtract 2 from each number, then the mean will be 7 – 2 = 5

Question 5.
If the mean of 6, 4, 7, a and 10 is 8. Find the value of ‘a’.
Solution:
No. of terms = 5
Mean = 8
∴ Sum of number (Σxi) = 5 x 8 = 40 …(i)
But Σxi = 6 + 4 + 7 + a+10 = 27 + a ….(ii)
From (i) and (ii)
27 + a = 40 ⇒ a = 40 – 27
∴ a = 13

Question 6.
The mean of the number 6, y, 7, x and 14 is 8. Express y in terms of x.
Solution:
No. of terms = 5 and
mean = 8
∴ Sum of numbers (Σxi) = 5 x 8 = 40 ….(i)
But sum of numbers given = 6 + y + 7 + x + 14
= 21 + y + x + ….(ii)
From (i) and (ii)
27 + y + x = 40
⇒ y = 40 – 27 – x
⇒ y= 13 – x

Question 7.
The ages of 40 students are given in the following table :
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 24 Measures of Central Tendency Ex 24A Q7.1
Find the arithmetic mean.
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 24 Measures of Central Tendency Ex 24A Q7.2

Question 8.
If 69.5 is the mean of 72, 70, x, 62, 50, 71, 90, 64, 58 and 82, find the value of x.
Solution:
No. of terms = 10
Mean = 69.5
∴ Sum of numbers = 69,5 x 10 = 695 ….(i)
But sum of given number = 72 + 70 + x + 62 + 50 + 71 + 90 + 64 + 58 + 82 = 619+x ….(ii)
From (i) and (ii)
619 + x = 695
⇒ x = 695 – 619 = 76

Question 9.
The following table gives the heights of plants in centimeter. If the mean height of plants is 60.95 cm; find the value of ‘f’.
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 24 Measures of Central Tendency Ex 24A Q9.1
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 24 Measures of Central Tendency Ex 24A Q9.2
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 24 Measures of Central Tendency Ex 24A Q9.3

Question 10.
From the data given below, calculate the mean wage, correct to the nearest rupee.
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 24 Measures of Central Tendency Ex 24A Q10.1
(i) If the number of workers in each category is doubled, what would be the new mean wage? [1995]
(ii) If the wages per day in each category are increased by 60%; what is the new mean wage?
(iii) If the number of workers in each category is doubled and the wages per day per worker are reduced by 40%. What would be the new mean wage?
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 24 Measures of Central Tendency Ex 24A Q10.2
(i) Mean remains the same if the number of workers in each catagory is doubled.
∴ Mean = 80.
(ii) Mean will be increased by 60% if the wages per day per worker is increased by 60%.
∴ New mean = 80 x \(\frac { 160 }{ 100 }\)= 128
(iii) No change in the mean if the number of worker is doubled but if wages per worker is reduced by 40%, then
New mean = 80 x \(\frac { 60 }{ 100 }\)= 48

Question 11.
The contents of 100 match boxes were checked to determine the number of matches they contained.
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 24 Measures of Central Tendency Ex 24A Q11.1
(i) Calculate, correct to one decimal place, the mean number of matches per box.
(ii) Determine how many extra matches would have to be added to the total contents of the 100 boxes to bring the mean up to exactly 39 matches. [1997]
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 24 Measures of Central Tendency Ex 24A Q11.2
(ii) In the second case,
New mean = 39 matches
∴ Total contents = 39 x 100 = 3900
But total no of matches already given = 3813
∴ Number of new matches to be added = 3900 – 3813 = 87

Question 12.
If the mean of the following distribution is 3, find the value of p.
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 24 Measures of Central Tendency Ex 24A Q12.1
Solution:
Mean = 3
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 24 Measures of Central Tendency Ex 24A Q12.2
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 24 Measures of Central Tendency Ex 24A Q12.3

Question 13.
In the following table, Σf= 200 and mean = 73. Find the missing frequencies f1 and f2.
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 24 Measures of Central Tendency Ex 24A Q13.1
Solution:
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 24 Measures of Central Tendency Ex 24A Q13.2
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 24 Measures of Central Tendency Ex 24A Q13.3

Question 14.
Find the arithmetic mean (correct to the nearest whole-number) by using step-deviation method.
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 24 Measures of Central Tendency Ex 24A Q14.1
Solution:
Let the Assumed mean = 30
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 24 Measures of Central Tendency Ex 24A Q14.2
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 24 Measures of Central Tendency Ex 24A Q14.3

Question 15.
Find the mean (correct to one place of decimal) by using short-cut method.
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 24 Measures of Central Tendency Ex 24A Q15.1
Solution:
Let the Assumed mean A = 45
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 24 Measures of Central Tendency Ex 24A Q15.2
Selina Concise Mathematics Class 10 ICSE Solutions Chapter 24 Measures of Central Tendency Ex 24A Q15.3

Hope given Selina Concise Mathematics Class 10 ICSE Solutions Chapter 24 Measures of Central Tendency Ex 24A are helpful to complete your math homework.

If you have any doubts, please comment below. Learn Insta try to provide online math tutoring for you.