ARITHMETICAL FORMULAE
In arithmetic various formulae are used to solve problems. Some Important ones are given below :
1. Operations with indices :
- x1. xm = x1+m when the bases are
- x1.x1 = (xy)1 when exponents are
- xm + xm = xm-n when bases are the
|
- xn yn = x
y
when exponents are same.
- (xm)n – xmn
- [(xm)n]1 = xmn1
2. Law of Surds
- nÖ
n
x = x
- nÖxnÖy = nÖxy
- mÖnÖa = mnÖa
- Prime numbers : Any natural number including 0 and 1 that can be divided only by 1 and by itself is known as prime number e.g. 3,5,7,11,13,17
Fraction ® p ®
number
q denominator
HCF, LCM and tests of divisibility have been given in chapter one.
POWERS OF TEN
1012 = 1000,000,000,000 ® one trillion
109 = 1000,000,000 ® one billion
106 = 1000,000 ® one million
105 = 100,000 ® one hundred thousand 104 = 10000 ® ten thousand
103 = 1000 ® one thousand
102 = 100 ® one hundred
101 = 10 ® ten
100 = 1 ® one
Note : In case of multiplication exponents are added e.g. (4 C 106) C (2 C 104)
= 8 C 1010
In case of division exponents are subtracted e.g. (4 C 106) ÷ (2 C 104) = 2 C 102
A power of numerator to denominator of 10 can be transferred from the numera- tor to denominator or vice versa by changing the sign of exponent e.g.
1/10-2 = 102, 10-5 = 1 .
105
5. PERCENTAGE, PROFIT, LOSS AND DISCOUNT
Percentage : A percentage is the fraction with its denominator 100 is equal to the percent as is the numerator i.e.
x% = x
100
Cost price or C.P. : It is the amount paid to purchase an item.
Other expenses like cartage, labour charges, taxes etc. all come in cost price.
Selling Price or S.P. : The amount received on selling an article is called its selling price.
Profit : S.P. – C.P. is the gain or profit.
Loss : C.P. – S.P. is the loss to the seller.
Gain or loss are always calculated on cost price.
Gain or loss percent : Gain or loss is always calculated on Rs. 100 and is called gain or loss percent.
- Gain % =Grain C 100
C.P.
- Loss % =Loss C 100
C.P.
(c) S.P. = 100 C gain % C C.P. 100
(d) S.P. = 100 – Loss % C C.P. 100
(e) C.P. = 100 C S.P.
100 + Gain %
(f) C.P. = 100 C S.P.
100 – Loss %
Trade discound : The reduction made on the marked price to the purchaser is called trade discount.
Net Price : Net price is defined as the price after deducting the trade discount
i.e.
Net price = Marked Price-Discount
Successive discounts : If two or more discounts are given one after the other
these are called successive discounts. e.g. successive discounts of 20% and 10% result Rs. 100 – 20 = 80
80 – 10% = 80 – 8 = 72
Net price becomes Rs. 72.
The discount is always given on the marked price. Successive discounts are attractive to the buyer but profitable to the seller e.g. two discounts of 20% and 10% come out to be only 28% to the purchaser. As a matter of fact purchaser thinks it 30% discount. In fact these are the tricks of business. Business people make lucarative offers to attract the purchasers.
