Ratio & Proportions- Aptitude Problems With Solutions Download

Ratio & Proportion


The ratio of two quantities; a & b in the same units is the fraction a/b and we write it as a: b

In the ration a: b, we call a as the first term or antecedent and b, the second term or consequent


The ratio 5: 9 represents the 5/9 value with antecedent = 5 and consequent = 9


The multiplication or division of each term of a ratio by the same no zero number does not affect the ratio.

Example – 4: 5 = 8: 10 = 12: 15 etc also 4: 6 = 2: 3



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 as mean terms.

Product of means = Product of extremes

Thus a: b : : c: d = ( b * c) = ( a * d)

Fourth proportional: if a: b = c: d, then d is called as the fourth proportional to a, b, c

Third proportional: if a: b = b: c, then c is called as the fourth proportional to a and b

Mean proportional: Mean proportional between a and b is root of ab. First calculate the multiplication of a and ab. After that, calculate the square root of the multiplication value.

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