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VOOZH | about |
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VOOZH | about |
In Class 8, Chapter 8 of the NCERT Mathematics textbook focuses on the "Comparing Quantities" a crucial concept in understanding proportional relationships and percentage calculations. Exercise 8.2 of this chapter deals with the problems involving simple and compound interest crucial for developing mathematical skills related to financial literacy. Mastering these exercises helps students grasp the fundamental principles of comparing quantities which are essential for solving real-world problems and further mathematical studies.
Comparing Quantities refers to evaluating and understanding the relative size or magnitude of two or more quantities. This concept is fundamental in various applications including financial calculations, statistical analysis, and everyday problem-solving. In Chapter 8 students learn how to use ratios, percentages, and proportions to make meaningful comparisons. Exercise 8.2 specifically enhances students' skills in calculating simple interest and understanding the impact of varying the interest rates and time periods.
Solution:
Let the initial salary was 100.
He got 10 % increment so increased salary is 110.
Increased salary(110%) is equal to 154000
Base salary(100%) is equal to 154000 × (100 / 110) = 140000
Hence his original salary was 140000.
Solution:
Given that On Sunday 845 people went to the Zoo.
On Monday only 169 people went.
Decrease in people = 845 - 169 = 676
Percentage decrease = (decrease / initial quantity) 100
= (676 / 845) × 100
= (0.8) × 100
= 80%
Hence percent decrease in the people visiting the Zoo on Monday is 80%.
Solution:
A shopkeeper buys 80 articles for 2,400
Cost price of one article is 2400 / 80 = 30
Percentage Profit = 16
Profit = (C.P. × Percentage Profit) / 100
Profit = (30 × 16) / 100
Profit = 4.8
Selling price of one article = C.P. + Profit
= (30 + 4.80)
= 34.80
Hence the selling price of one article is 34.80.
Solution:
Total cost of an article after repair = Cost + repair expenses
= 15500 + 450
= 15950 rupees
Profit percent = 15
Profit = (C.P. × Percentage Profit) / 100
Profit = (15950 × 15) / 100 = 2392.50
Selling price of the article = C.P. + Profit
= (15950 + 2392.50)
= 18342.50
Hence the selling price of the article is 18342.50
Solution:
C.P. of a VCR = 8000
C.P. of a TV = 8000
As the cost price of both the article are same so profit and loss calculated on same cost price would be same
so effective profit / loss = (8% profit - 4% loss)
= 4% profit
So gain = C.P. (profit / 100)
= 8000 (4 / 100)
= 320
Hence the gain percent on the whole transaction is 320.
Profit % on the whole transaction = (Profit / Total CP) x 100
= (320 / 16000) x 100
= 2%
Solution:
As the discount is offered on all the article by the shopkeeper so discount can be calculated from total marked price.
So Total marked price = (1,450 + 2 × 850)
= (1,450 + 1,700)
= 3,150
Given that, discount percentage = 10%
Discount = (3150 ×10 ) / 100 = 315
Also, Sale price = Marked price - Discount
Sale price = (3150 − 315)
= 2835
Hence the customer will have to pay 2,835.
Solution:
Let us consider C.P. of buffaloes are 100 each
On one he made a gain of 5%
if C.P. is 100 Then S.P.= 105
So cost price = (C.P. / S.P.) 20000
= (100 / 105) 20000
= 19,047.62
on the other a loss of 10 %
if C.P. is 100 Then S.P. = 90
∴ C.P. of other buffalo = (100 / 90) × 20000
= 22222.22
Total C.P. = 19047.62 + 22222.22
= 41269.84
Total S.P. = 20000 + 20000 = 40000
Loss = 41269.84 − 40000 = 1269.84
So the overall loss of milkman was 1269.84
Solution:
Let C.P. is 100
the tax to be paid = 12
The tax to be paid will be on 13000 = (12 / 100) × 13000
= 1560
Required amount to pay = Cost + Sales Tax
= 13000 + 1560
= 14560
Hence Vinod will have to pay 14,560 for the T.V.
Solution:
Let the marked price of the article is 100
Discount given = 20
S.P. = (100 - 20) = 80
when assumed S.P. is 80 actual S.P.is 1600
then marked price 100 is =1600 × (100 / 80)
= 2000
Hence the marked price was 2000.
Solution:
Let the original price is 100
then price including VAT will be 108.
When price including VAT is 108
Then original price = 100
When price including VAT is 5400, original price = (100 / 108) × 5400
= 5000
Hence the price of the hair-dryer before the addition of VAT was 5000.
Solution:
Let the original price of article excluding GST was 100
After including GST purchased price will be 118
So 118% ( including GST ) = 1239
100% ( excluding GST ) = 1239 × (100 / 118)
= 1050
Hence the price of the article before GST was added was 1050.
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