IMPORTANT FACTS AND FORMULAE
I. RATIO :: The ratio of the two quantities say a and b in the same units, is the fraction a/b and we write it or we denote it as-
a:b.
In the ratio a:b,
a - antecedent. (first term)
b - consequent. (second term)
Ex. The ratio 5: 7 represents 5/7 with antecedent = 5, consequent = 7.
Rule :: The multiplication or division of each term(both antecedent and consequent) of a ratio by the same non-zero number does not affect the ratio.
Ex. 4: 6 = 8: 12 = 12: 24 etc. Also, 4: 6 = 2: 3.
2. PROPORTION :: It is define as the equality of two ratios is called proportion.
If a: b = c: d, we can write it as, a: b:: c : d and we say that a, b, c, d are in proportion. Here a and d are called extremes terms, while b and c are called mean terms.
a and d = extremes terms.
b and c = 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 here d is called as the fourth proportional to a, b, c.
(ii) Third Proportional :: If a: b = b: c, then here c is called as the third proportional to a and b.
(iii) Mean Proportional :: Mean proportional between a and b is the square root of ab
4. (i) COMPARISON OF RATIOS ::
(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) x is directly proportional to y, if x = ky for some constant L and we write it as,
x ∞ y.
(ii) x is inversely proportional to y, if xy = k for some constant L and we write,
x∞(1/y)
Written
In Aptitude, Concepts, Ratio And Proportion
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