Problems on Ratio and Proportion PART-1

1 If P : Q : R = 2 : 3 : 4 , Then P / Q : Q / R : R / P = ?

A. 8: 9: 24

B. 7: 9: 24

C. 4: 6: 15

D. 8: 11: 24

E. None of these

2: If 2P = 3Q = 4R, Then P : Q : R = ?

A. 2: 3: 5

B. 2: 3: 4

C. 3: 5: 6

D. 1: 2: 3

E. None of these

3: If P : Q = 2 : 3 , Q : R = 4 : 5 and R : S = 6 : 7 , then P : S = ?

A. 18: 25

B. 17: 35

C. 16: 35

D. 8: 11

E. None of these

4: 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?

A. 66

B. 64

C. 72

D. 77

E. None of these

5: Two numbers are respectively 40% and 60% more than the third number. Find the ration of two numbers?

A. 8: 7

B. 7: 9

C. 9: 11

D. 8: 13

E. None of these

Solutions :

1. 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
R / P = 4k / 2k = 2 / 1.

SO, P / Q : Q / R : R / P = 2 / 3 : 3 / 4 : 2 / 1 = 8 : 9 : 24.

2. 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 = 6 : 4 : 3.

3. (C)

4. 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 a minimum number of pencils x = 1 .
The person should have at least 77 pencils.

5.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.