Ratios and Proportions Questions
FACTS AND FORMULAE FOR RATIO AND PROPORTION QUESTIONS
1. 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
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 .
(ii) Sub-duplicate ratio of (a : b) is (√a : √b).
(iii)Triplicate ratio of (a : b) is .
(iv) Sub-triplicate ratio of (a : b) is .
(V) (Componendo and dividendo)
(i) We say that x is directly proportional to y, if x = ky for some constant k and we write,
(ii) We say that x is inversely proportional to y, if xy = k for some constant k and we write,