Ratio and ProportionRatio:
- The ratio of two quantities a and b of same units is the fraction x/y, where b ≠ 0
- The fraction x/y can be represented as x:y Different types of ratios are:1) Duplicate ratio:
It is the ratio of squares of two numbers.
2) Sub-duplicate ratio:
|Duplicate ratio of the fraction ||x|| is given as: ||x|| = ||x2|| or x : y = x2 : y2|
It is the ratio between square roots of two numbers.
3) Triplicate ratio:
|Duplicate ratio of the fraction ||x|| is given as: ||x|| = ||x|| or x : y = x : y|
It is the ratio of cubes of two numbers.
4) Sub- Triplicate ratio:
|Triplicate ratio of the fraction ||x|| is given as ||x|| = ||x3|
It is the ratio between cube roots of two numbers
5) Compound ratio:
|Sub-Triplicate ratio of the fraction ||x|| is given as ||x|| = ||x(1/3)|
It is the ratio of product of first terms in every ratio to that of product of second term in every ratio.
Compound ratio of (a : x), (b : y), (c : z) is (abc : xyz)6) Inverse ratio:
The ratio formed by interchanging their old places in the ratio to new
The inverse ratio of 5 : 8 is 8 : 5.Proportion: 1)
Proportion is the equality of two ratios.
When (a : b = x : y) is represented as (a : b :: x : y), then a, b, x, y are said to be in proportion.
In (a : b :: x : y),
a and y are called as extremes
and b and x are called as mean terms. Product of means = Product of extremes2)
Mean proportion: Mean proportion between x and y is given as xy3)
Third proportion: If p : q = q : s, then s is called as third proportional to p and q. 4)
Fourth proportion: If u : v = x : y, then y is the fourth proportional of u, v and x.Quick Tips and Tricks1) Comparison of ratios:
2) Proportion4) Variation:
|If (x : y) > ( a : b) → ||x|| > ||a|
- If a = kb for some constant k, then we can say that a is directly proportional to b.
- If ba =k for some constant k, then we can say that a is inversely proportional to b. 5)
If ratio between first and second quantity m : n = a : x,
second and third quantity n : p = b : y,
fourth and fifth quantity p : q = c : z,
then m : n : p : q
can be easily solved by using the trick shown below: m : n : p : q = abc : xbc: xyc : xyz6)
If a number a is divided in the ratio x : y,
Question VarietyExamples:Q 1.
|2) Second part: ||ay|
|(x + y)|
If a : b = 2 : 3 and b : c = 5 : 7, then find a : b : c.
a. 12 : 15 : 9
b. 10 : 15 : 21
c. 14 : 12 : 21
d. 2 : 15 : 7View solution
Correct option : (b)
Here, to find a : b : c, use the trick discussed in quick tips and tricks.
a : b : c = (2 x 5) : ( 3 x 5) : (3 x 7) = (10) : (15) : (21)
If A : B : C = 3 : 4 : 7, then what is the ratio of (A / B) : (B / C) : (C / A)?
a. 63 : 48 : 196
b. 66 : 49 : 190
c. 56 : 40 : 186
d. 46 : 38 : 160View solution
Correct option : (a)
Hint: If a = kb for some constant k, then we can say that a is directly proportional to b.
A : B : C = 3 : 4 : 7
Assume, A = 3 k, B = 4 k, C = 7 k
|A|| = ||(3k)||, ||B|| = ||(4k)||, ||C|| = ||(7k)|
|A|| = ||(3)||, ||B|| = ||(4)||, ||C|| = ||(7)|
L.C.M of 3, 4, 7 is 84
(3 x 84) / 4 = 63
(4 x 84) / 7 = 48
(7 x 84) / 3 = 196Ratio of (A/B) : (B/C) : (C/A) = 63:48:196