FORMULAE
I. RATIO: The ratio of two quantities a and
b in the same units, is the fraction a/b and we write it
as a:b.
In the ratio a:b, we call a as the first term or
antecedent and b, the second
term or consequent.
Ex. The ratio 5: 9 represents 5/9 with antecedent =
5, consequent = 9.
Rule: The multiplication or division of each term
of a ratio by the same non-zero number does not
affect the ratio.
Ex. 4: 5 =
8: 10 = 12: 15 etc. Also, 4: 6 = 2: 3.
2. PROPORTION:
The equality of two ratios is called
proportion.
If a: b =
c: d, we write, a: b:: c : d
and we say that a, b, c, d are
in proportion . Here a
and d are called extremes, while b and c are called mean terms.
Product of means =
Product of extremes.
Thus, a: b:: c : d <=> (b x c) = (a x d).
3. (i) Fourth Proportional: If a : b = c: d, then d is called the fourth proportional to
a, b, c.
(ii) Third Proportional: If a: b = b: c, then c is called the
third proportional to a
and b.
(iii) Mean
Proportional: Mean proportional between a
and b is square root of ab
4. (i) COMPARISON OF RATIOS:
We say that (a: b) > (c: d) <=> (a/b)>(c /d).
(ii)
COMPOUNDED RATIO:
The
compounded ratio of the ratios (a: b),
(c: d), (e : f) is (ace: bdf)
5. (i) Duplicate
ratio of (a : b) is (a2 : b2).
(ii) Sub-duplicate ratio of (a : b) is (√a : √b).
(iii)Triplicate ratio of
(a : b) is (a3 : b3).
(iv)
Sub-triplicate ratio of (a : b)
is (a ⅓ : b
⅓ ).
(v)
If (a/b)=(c/d), then
((a+b)/(a-b))=((c+d)/(c-d)) (Componendo
and dividendo)
6. VARIATION:
(i) We say that x is directly proportional to y, if x = ky for some constant k
and
we write,
x ยต y.
(ii) We
say that x is inversely proportional to y,
if xy = k for some
constant k and
we write, x∞(1/y)
OR 