 Explanation / Important formulas:

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.
• Example: 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.]

Example:  4 : 5 = 8 : 10 = 12 : 15. Also, 4 : 6 = 2 : 3.

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).

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

Third Proportional: a : b = c : d, then c is called the third proportion to a and b.

Mean Proportional: Mean proportional between a and b is ab.

Comparison of Ratios: We say that (a : b) > (c : d) <=> a / b > c / d

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

Duplicate Ratios: 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 (a1/3 : b1/3).
•  If a/b = c/d, then a + b / a – b =c + d / c – d [Componendo and dividendo]

Variations

• We say that x is directly proportional to y, if x = ky for some constant k and we write, x ∝ y.
• We say that x is inversely proportional to y, if xy = k for some constant k and we write, x ∝ 1/ y

Instructions to take Aptitude Test

• Click on start to start taking the test.
• Click on the option (A, B, C or D) to figure out the right answer.
• You can answer multiple times till you get the right answer.
• Once you get the right answer, explanations (if any) for the same will be showcased down.
• On click of list, you get to see total no of questions, no of questions you answered and no of questions pending to answer.
• On click of question number you will go to that particular question.
• On click of END your test will end.
• On click of ‘Get Results’ you will get to see correct answer for each questions.