## Ratio Example 1

### Example 1:

If P : Q : R = 2 : 3 : 4 , Then P / Q : Q / R : R / P = ?
P : Q : R = 2 : 3 : 4 . Let P = 2k, Q = 3k, R = 4k. Then,
P / Q = 2k / 3k = 2 / 3 , Q / R = 3k / 4k = 3 / 4 and R / P = 4k / 2k = 2 / 1.
SO, P / Q : Q / R : R / P = 2 / 3 : 3 / 4 : 2 / 1 = 8 : 9 : 24 .

### Example 2:

If P : Q = 2 : 3 and Q : R = 4 : 5 , then R : P = ?
P / R = ( P / Q x Q / R ) = ( 2 / 3 x 4 / 5 ) = 8 / 15
=R / P = 15 / 8 = R : P = 15 : 8.

### Example 3:

If 2P = 3Q = 4R, Then P : Q : R = ?
Let 2P = 3Q = 4R = k , Then , P = k / 2, Q = k / 3 , R = k / 4.
SO , P : Q : R = k / 2 : k / 3 : k / 4 = 2 : 3 : 4

### Example 4:

If a : b = 3 : 7 and b : c = 5 : 9, find a : b : c .
Answer:  A : B = 3 : 7, B : C = 5 : 9
= ( 5 x 7 / 5 ) : ( 9 x 7 / 5 ) = 7 : 63 / 5 .
= A : B : C = 3 : 7 : 63 / 5 = 15 : 35 : 63 .

### Example 5:

If P : Q = 2 : 3 , Q : R = 4 : 5 and R : S = 6 : 7 , then P : S = ?
P / S = ( P / Q x Q / R x R / S ) = ( 2 /3 x 4 / 5 x 6 / 7 ) = 16 / 35 = P : S = 16 : 35 .

### Example 6:

If P : Q = 1 / 2 : 3 /8 , Q : R = 1 / 3 : 5 / 9 and R : S = 5 / 6 : 3 / 4 , Then P : Q : R : S = ?
P : Q = 1 / 2 : 3 / 8 = 4 : 3 , Q : R = 1 / 3 : 5 / 9 = 3 : 5 and R : S = 5 / 6 : 3 / 4 = 10 : 9
P : Q = 4 : 3 , Q : R = 3 : 5 , R : S = 10 / 2 : 9 / 2 = 5 : 9 / 2
P : Q : R : S = 4 : 3 : 5 : 9 / 2 = 8 : 6 : 10 : 9 .

### Example 7:

Rama distributes his pencil among his four friends Rakesh, Rahul, Ranjan, and Rohit in the ratio 1 / 2 : 1 / 3 : 1 / 4 : 1 / 5 . What is the minimum number of pencils that the person should have?
Rakesh : Rahul : Ranjan : Rohit = 1 / 2 : 1 / 3 : 1 / 4 : 1 / 5
Step 1: At First we need to do is LCM of 2,3,4 and 5 is 60.
Step 2: Then pencil are distributed in ratio among friends,
Rakesh = ( 1 / 2 x 60 ) = 30.
Rahul = ( 1 / 3 x 60 ) = 20.
Ranjan = ( 1 / 4 x 60 ) = 15.
Rohit = ( 1 / 5 x 60 ) = 12.

Step 3: Total number of pencils are ( 30 x + 20 x + 15 x + 12 x) = 77 x.
For minimum number of pencils x = 1 .
The person should have atleast 77 pencils.

### Example 8:

Two numbers are respectively 40% and 60% more than third number.Find the ration of two numbers ?
Step 1: Let the third number is A
Then first number is 140% of A = 140 x A / 100 = 7A / 5 and second number is 160% of B = 160 x B / 100 = 8B / 5.
Step 2: now ratio of first and second number is 7A / 5 : 8B / 5 = 35A : 40B = 7 : 8.

### Example 9:

If 75 is divided into three parts proportional to 3, 5, 8, 9 then the smallest part is :