Page 189 - Math_Genius_V1.0_C8_Flipbook

E:\Working\Focus_Learning\Math_Genius-8\Open_Files\09_Chapter_7\Chapter_7
\ 06-Jan-2025 Bharat Arora Proof-7 Reader’s Sign _______________________ Date __________

Encapsulate
math
CoMPARING QUANTITIES

Percentage of a Number Discount
To find the percentage (P%) of a number or quantity • Discount = Marked Price (MP) – Selling Price (SP)
P Discount
(Q), we use the formula P% of Q = × 100. • Discount % = × 100%
100 MP

Taxes
Increase or Decrease in Per cent • Sales Tax: Tax collected by shopkeeper from the
Percentage increase/decrease purchaser at the time of selling the goods and is
Change in value (increase or decrease) deposited to government is called sales tax.
= × 100%
Original value Bill amount = Selling price + Sales tax
• Value Added Tax (VAT): It is charged as a certain
percentage of the selling price of an item.
Profit and Loss • Goods and Service Tax (GST): It is an indirect tax
imposed on the supply of goods and services.
• The amount paid to purchase an article is called
its cost price.
• The amount at which an article is sold is called its Compound Interest
selling price. Interest calculated on previous year’s amount.
CI = A – P
• Overhead expenses are included while buying where A = amount, P = principal, CI = compound
or selling goods. For example: Cartage, labour interest.
charges, etc.
Formulae
• When interest is compounded annually
Formulae  R  n   R  n 

• Profit = SP – CP • Loss = CP – SP A = P 1 + 100  , CI = P      1 + 100  − 1  

Profit Loss • When interest is compounded half-yearly
• Profit% = × 100% • Loss % = × 100%
CP CP  R  2n   R  2n 

 100 + P%  A = P 1 + 200  , CI = P    1 + 200  − 1

• SP =   × CP , when profit% is given    
 100  • When interest is compounded quarterly
 100 − L%   R  4n   R  4n 
• SP =   × CP, when loss% is given A = P 1 + , CI = P  1 + − 1
 100    400      400   

Mental Maths
9
1. What percentage is equivalent to ?
25
2. The marked price of a bottle is `250 and the discount per cent is 20%. What is the selling price of the bottle?
3. Shubham bought a jacket for `1,280. Find its selling price if it is sold at 10% gain.
4. A certain sum of money is doubled in 7 years at a fixed rate of interest compounded yearly. In how many
years will it be four times?
5. The price of an article is first increased by 30% and then decreased by 30%. What will be the new price with
respect to the initial price?
6. If the CP of 5 articles is equal to the SP of 4 articles, then what would be the profit or loss per cent in this
transaction?

187 Comparing Quantities