Ratio and Proportion Formulas, Shortcuts, Example Questions

Ratio and Proportions

Ratio: It means comparison of two quantities by division [or] It means what part one quantity is of another quantity.
Points to Remember:
• When comparing two quantities they must be expressed in same units.
• Ratio doesn't change if both the terms are multiplied or divided by same number.
• If four quantities are in proportion, then Product of Means = Product of Extreams.
• Ex: a:b::c:d ==> bc = ad
• If a, b, c and d are in proportion , then
• 4th proportion ==> d = (bc)/a
• 3rd proportion ==> c = (ad)/b
• Mean Proportion between a & b is given by x =  ab
• If in given problem A:B & B:C given, asked to find A:B:C then

•  If in given problem A:B, B:C & C:D are given and asked to find A:B:C:D then

Example Problems:
1. Find the Mean proportion between 48 and 12?
A) 28                            B) 24                          C) 34                                 D) 26

Ans. B
Solution:
Consider 'X' is mean proportion of a & b
X =   ab
X =   48*12
X =   576
X = 24

2. Two numbers are in the ratio of 4:5 and the sum is 27. Find the two numbers?
A) 12, 15                        B) 20, 7                        C) 7, 20                   D) 15, 12

Ans. A
Solution:
4x + 5x = 27;
9x = 27;
x = 3;
4x : 5x = 4(3) : 5(3);
4x : 5x = 12 : 15.

3. Three numbers are in the ratio of 3:4:8. and the sum of three numbers is 975. Find the numbers?
A) 520, 560, 195                                 B) 520, 195, 560
C) 195, 560, 520                                 D) 560, 520, 195

Ans. C
Solution:
3x + 4x + 8x = 975;
15x = 975;
x = 65;
3x : 4x : 5x = 3(65) : 4(65) : 8(65);
= 195 : 260 : 520.

[OR]

First Number = [3/(3+4+8)] * 975 = 195
Second Number = [4/(3+4+8)] * 975 = 260
Third Number = [8/(3+4+8)] * 975 = 520

4. Two numbers are in the ratio of 4:5. and the difference between two numbers is 24. Find the numbers?
A) 100, 124                                           B) 120, 96
C) 96, 120                                             D) 124, 100

Ans. D
Solution:
5x - 4x = 24;
x = 24;
4x : 5x = 4(24) : 8(24);
4x : 5x = 96 : 120.

5. Two numbers are in the ratio of 3:4. If 8 is added to each of the number then ratio becomes 5:6. Find the two Numbers?
A) 12, 16                          B) 16, 12          C) 9, 12                           D) 12, 9

Ans. A
Solution:
Consider the Two numbers 3x & 4x
From Ratio & Proportion
3x + 8 : 4x + 8 :: 5 : 6
5 * (4x + 8) = 6 * (3x + 8)
20x + 40 = 18x + 48
2x = 8
x = 4
3x : 4x = 3(4) : 4(4)
3x : 4x = 12 : 16.

6. Two numbers are in the ratio of 5:9. If each number is decreased by 5 then ratio becomes 5:11. Find the two Numbers?
A) 27, 15                          B) 15, 27          C) 20, 36                           D) 25, 45

Ans. B
Solution:
Consider the Two numbers 5x & 9x
From Ratio & Proportion
5x - 5 : 9x - 5 :: 5 : 11
5 * (9x - 5) = 11 * (5x - 5)
45x - 25 = 55x - 55
10x = 30
x = 3
5x : 9x = 5(3) : 9(3)
5x : 9x = 15 : 27.

7. If A:B = 2:3, B:C = 4:5 then find A:B:C?
A) 8:12:15                                                          B) 4:6:15
C) 12:8:15                                                          D) 8:12:15

Ans. A
Solution:
8 : 12 : 15

8. If A:B = 2:3, B:C = 4:5, C:D = 6:7 then find A:B:C:D?
A) 16:24:30:35                                                B) 24:16:30:35
C) 16:30:24:35                                               D) 16:35:30:24

Ans. A
Solution:
16 : 30 : 24 : 35