Aptitude - Ratio and Proportion

Ratio

The ratio of two quantities a and b in the same units, is a fraction that one quantity is of the other. Thus, ab = a : b

In a : b, we call a as antecedent and b as consequent.

Rule : The multiplication or division of each term of a ratio by the same non-zero number does not affect the ratio.
Thus, 4 : 5 is the same as 8 : 10 or 12 : 15

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 extrvares, while b and c are called mean terms.

Rule : Product of means = Product of extrvares.
Thus, a : b :: c : d ⇔ (b x c) = (a x d)

Fourth Proportional

If a : b = c : d, then d is called the fourth proportional to a, b, c

Third Proportional

If a : b = c : d, then c is called the third proportional to a and b

Mean Proportional

Mean Proportional between a and b is √ab

Compounded Ratio

The compounded ratio of the ratios (a : b), (c : d), (e : f) is (ace : bdf)

Componendo and Dividendo

If ab = cd, then a + ba − b = c + dc − d

Duplicate ratio of (a : b) is (a² : b²)

Sub-duplicate ratio of (a : b) is (√a : √b)

Triplicate ratio of (a : b) is (a³ : b³)

Sub-triplicate ratio of (a : b) is (a^1/3 : b^1/3)