Introduction

Quantitative Analysis requires a lot of practice and hardwork since its an analytical subject. Before becoming an expert one should understand the basics of Quantitative Analysis for Government Bank Job Exams for SBI, RBI, RRB and IBPS. This section gives you all details about the basics of Quantitative Analysis. Here you can get the Free Notes and PDF downloads for Quantitative Analysis to prepare for the Bank PO and Clerical Jobs in India. Our experts are available incase you need any kind of online help to understand any topic or any kind of doubt clearing

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10. RATIO AND PROPORTION

 

A. 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.

B. 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).

C. (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

D. (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)

E. (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)

F. VARIATION :

(i) We say that x is directly proportional to y, if x = ky for some constant k and we write, x ∞ y.
(ii) We say that x is inversely proportional to y, if xy = k for some constant k and we write, x∞(1/y)

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