ARITHMETIC
FUNDAMENTALS
ü
In
this chapter, we shall study comparing quantities like ratio and proportion,
profit and loss, discount simple interest, distance speed and time.
Ratio
and Proportion
ü
Ratio
is a method of comparing two quantities of the same kind by division.
ü
When
two ratios are equal, they are said to be in proportion.
ü
If
two ratios are to be equal or are in proportion, their product of means should
be equal to the product of extremes.
Example: If a: b: c: d then the
statement ad = be, holds good.
If
a: b and b: c are in proportion such that \[{{b}^{2}}\]=
Ac
than b is called the mean proportional of a: b and b: c
ü
Multiplying
or dividing terms of the ratio by the same number gives equivalent ratios.
Elementary
Questions
Q. If\[5:6=a:18\],
then\[a=?\]?
Sol. \[\frac{5}{6}-\frac{a}{18}=5\times
18=a\times 6\]
\[\Rightarrow
a=\frac{5\times 15}{6}=15\]
Elementary
Question:
Q. \[\frac{37}{25}\]can
also be written as,
(a)\[\frac{147}{99}\] (b)\[\frac{149}{101}\] (c)\[\frac{148}{100}\] (d)\[\frac{152}{97}\]
Sol. \[\frac{37}{25}=\frac{37\times
4}{25\times 4}=\frac{148}{100}\]
Percentage
ü
Another
way of comparing quantities is percentage. The word percent means per hundred.
Thus 12% means 12 parts out of 100 parts
ü
Fractions
can be converted into percentages and vice= versa.
Example:\[\frac{2}{5}=\frac{2}{5}\times 100%=40%\]
(ii)\[25%=\frac{25}{100}=+\frac{1}{4}\]
ü
Decimals
can be converted into percentages and vice-versa.
Example:
(i)\[0.36=0.36\times 100%\]
(ii) \[43%=\frac{43}{100}=0.43\]
Simple
Internet
ü
When
we deposit money in banks, bank give interest on money. Interest may be simple
interest (called S.I.)
A= Amount
B= Principle
R= Rate
T= Time
\[S.I.=\frac{P\times R\times T}{100}\]
(Simple Interest)\[S.I.=A-P\]