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Ratio and Proportion - Introduction
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Some basic concepts regarding ratios and proportions that are essential for problem solving.

Ayushi gupta
I am Ayushi Gupta, final year MBA Marketing student. I have done my engineering in computer science. With my experience in recruitment proce

Unacademy user
mam teaching informal bhi to ho sakta hee so 1 q answer ni huya
please get some more topics

  2. Ratio: The ratio of two quantities a and b in the same units, is the fraction write it as a b b and we In the ratio a b, we call a as the first term or antecedent and b, the second term or consequent. Eg. The ratio 5:9 represents 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 Eg. 4 : 5 = 8 : 10=12:15 Also, 4 : 6-23.

  3. Example 1 What is the ratio of 2 feet to 4 yards? Solution: The ratio cannot be formed until the numbers are expressed in the same units. Let's turn the yards into feet. Since there are 3 feet in a yard, 4 yards-4 * 3 feet = 12 feet 2feet--|or 1 : 6 Forming the ratio yields 12 feet The answer is (D).

  4. 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) = (axd). 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)^1/2.

  5. Comparison of Ratios: We say that a (a: b)(cd) b Compounded Ratio: The compounded ratio of the ratios: (a : b), (c: d), (e f is (ace: bdf).

  6. Duplicate Ratios: Duplicate ratio of (a : b) is (a*: b-) Sub-duplicate ratio of (a : b) is Triplicate ratio of (a: b) is (z? :G,5). > Sub-triplicate ratio of a: b) is (al /3 : b1/3) (componendo and If dividendo) =-, then = a-b c-d

  7. Variations: We say that x is directly proportional toy, if x = ky for some constant k and we write, X oc Y- We say that x is inversely proportional to y, if xy k for some constant k and we write, x CC