Ratio & Proportion

Question 1

Define Ratio

Answer 1

Ratio is a way of Comparison

Question 2

A ratio should be in ___ way

Answer 2

Same kind and same unit

Question 3

Position of antecedent in ratio

Answer 3

1st part of the ratio

Question 4

Position of consequent in ratio

Answer 4

2nd part of ratio

Question 5

Types of ratio

Answer 5

(A) Proper and improper ratio
(B) Compound ratio or mixed ratio, Inverse ratio, Duplicate ratio, Sub duplicate ratio, Triplicate ratio, Sub triplicate ratio

Question 6

What is proper ratio with ex

Answer 6

It is the ratio where antecedent is less than consequent ex 2:3

Question 7

What is improper ratio with ex

Answer 7

It is the ratio where antecedent is greater than consequent ex 3:2

Question 8

2:3 is ___ type of ratio

Answer 8

proper ratio

Question 9

3:2 is ___ type of ratio

Answer 9

Improper ratio

Question 10

Formula to write ratio into fraction

Answer 10

Fraction of antecedent = exact value / total value

Fraction of consequent = exact value / total value

Question 11

What does K means in ratio in detail through an example

Answer 11

• Value of two variables a & b = 5000 & 6000 respectively
• In constant of proportionality, it is 5K:6k

Reference:
- In ratio, it is 5:6
- In common multiplier or scalling factor, K = 1000
Through two values, in constant of proportionality we finds proportion of the ratio with each other and the common multiplier has the scalling factor.
So constant of proportionality and common multiplier are not one and the same.

Question 12

Ratio converting into Square is called as ___ (a:b into a² : b²)

Answer 12

Duplicate ratio

Question 13

Ratio converting into Cube is called as ___ (a:b into a³ : b³)

Answer 13

Triplicate ratio

Question 14

Ratio converting into Square root is called as ___ (a:b into 2√a:2√b)

Answer 14

Sub Duplicate ratio

Question 15

Ratio converting into Cube root is called as ___ (a:b into 3√a:3√b)

Answer 15

Sub Triplicate ratio

Question 16

Mixed ratio and ___ are same

Answer 16

Compound ratio

Question 17

What is concept of K in terms of constant of proportionality

Answer 17

(Doubt exist in this below explaination at 4th & 5th line)
- Value of two variables a & b = 5000 & 6000 respectively
- In ratio, it is 5:6
- In constant of proportionality, it is 5K:6k
[a = Kb -> k = a/b;
b = Ka -> k = b/a]

Through two values, constant of proportionality finds proportion of the ratio with each other.

Question 18

1st part of the ratio is called as ___

Answer 18

antecedent

Question 19

2nd part of ratio is called as ___

Answer 19

consequent

Question 20

In ___ antecedent is less than consequent with ex

Answer 20

proper ratio ex: 2:3

Question 21

In ___ antecedent is greater than consequent with ex

Answer 21

improper ratio ex 3:2

Question 22

Ex of proper ratio.

Answer 22

2:3

Question 23

Ex for improper ratio

Answer 23

3:2

Question 24

Fraction of antecedent in the ratio of 5:6

Answer 24

exact value / total value = 5/11

Question 25

Fraction of consequent in the ratio of 5:6

Answer 25

exact value / total value = 6/11

Question 26

___ means constant of proportionality

Answer 26

Concept of K

Question 27

Duplicate ratio converts the ratio into ___ (a:b into ___)

Answer 27

a:b into a² : b²

Question 28

Triplicate ratio converts the ratio into ___ (a:b into ___)

Answer 28

a:b into a³ : b³

Question 29

Sub Duplicate ratio converts the ratio into ___ (a:b into ___)

Answer 29

a:b into 2√a:2√b

Question 30

Sub Triplicate ratio converts the ratio into ___ (a:b into ___)

Answer 30

a:b into 3√a:3√b

Question 31

___ and Compound ratio are same

Answer 31

Mixed ratio

Question 32

What is concept of K in terms of common multiplier in ratio through an example

Answer 32

- Value of two variables a & b = 5000 & 6000 respectively - In ratio, it is 5:6 - In common multiplier or scalling factor, K = 1000 On those two values, the common multiplier has the scalling factor.

Question 33

Compound ratio ex

Answer 33

a:b, x:y ax : by ie: 2:3, 4:5 2x4 : 3x5 8:15

Question 34

Inverse ratio

Answer 34

Type1: a:b = 1/a : 1/b = b:a Type2: a:b:c = 1/a : 1/b : 1/c = bc:ac:ab / abc = bc:ac:ab

Question 35

When a, b, c, d is given, then proportion structure will be

Answer 35

a÷d : : b÷c -> a:d : : b:c or a = bxc ÷ d

Question 36

Proportion is similar to

Answer 36

Fraction

Question 37

In ratio fraction is similar to

Answer 37

Proportion

Question 38

When a, b, c is given, to find x, which is 1st proportion, then x =

Answer 38

x:a : : b:c => x = axb ÷ c

Question 39

In proportion a:b : : c:d, “a” needs to be find, then a =

Answer 39

a = bxc ÷ d

Question 40

When a, b, c is given, to find x, which is 2nd proportion, then x =

Answer 40

a:x : : b:c => x = axc ÷ b

Question 41

When a, b, c is given, to find x, which is 3rd proportion, then x =

Answer 41

a:b : : x:c => x = axc ÷ b

Question 42

When a, b, c is given, to find x, which is 4th proportion, then x =

Answer 42

a:b : : c:x => x = bxc ÷ a

Question 43

When a, b is given, to find x, which is 1st proportion, then x =

Answer 43

x:a : : a:b => x = a² ÷ b

Question 44

When a, b is given, to find x, which is 2nd proportion, then x =

Answer 44

When two numbers are given and ask for 2ⁿᵈ proportion. Here there is no 2ⁿᵈ proportion, because it is not possible. The structure will be a:x : : x:b

Question 45

When a, b is given, to find x, which is 3rd proportion, then x =

Answer 45

a:b : : b:x => x = b² ÷ a

Question 46

If 4 = 3x16 ÷ 12, then proportion structure can be

Answer 46

4:3 : : 16:12

Question 47

When a, b, c is given, to find mean proportion

Answer 47

b² = ac or b = √ac

Question 48

When a, b, c is given, then proportion structure will be

Answer 48

a÷b : : b÷c -> a:b : : b:c

Question 49

a÷b : : b÷c -> a:b : : b:c, this is the proportion structure of

Answer 49

This is the proportion structure when a, b, c is given and

Question 50

a÷b : : c÷d -> a:b : : c:d, this is the proportion structure of

Answer 50

This is the proportion structure when a, b, c, d is given and

Question 51

Proportion after addition formula, x

Answer 51

x = bc-ad ÷ (a+d)-(b+c)

Question 52

Proportion after subtraction formula, x

Answer 52

x = ad-bc ÷ (a+d)-(b+c)

Question 53

Concept of K means concept of proportionality but when adding value to K then it means ___

Answer 53

common multiplier with scaling factor.

Question 54

In the concept of K the common multiplier has ___

Answer 54

Scaling factor

Question 55

In ratio scaling factor is related to

Answer 55

Concept of K in term of common multiplier.

Question 56

___ is exact opposite to proportion in term of expression

Answer 56

Compound ratio Because, a proportion structure will be a:d : : b:c a compound ratio structure will be a:c : : b:d