# RRB NTPC - Ratios and Proportions (114 Questions with Explanation)

1.

Find the fourth proportional to 2.4, 4.6 and 7.6?

A.) 14
B.) 14.657
C.) 15.56
D.) 14.56

Formula = Fourth propotional = (b × c)/a
A = 2.4 , B = 4.6 and C = 7.6
(4.6 × 7.6)/2.4 = 14.56

2.

Find the third proportional to 9 and 12?

A.) 9
B.) 108
C.) 16
D.) 9

Formula = Third proportional = (b × b)/a
A = 9 and B = 12
(12 × 12)/ 9 = 144/9 = 16

3.

Find the mean proportional between 49 & 81?

A.) 16
B.) 10
C.) 63
D.) 12

Formula = √a×b
A = 49 and B = 81
√49×81 = 7 × 9 = 63

4.

Find the fourth proportional to 0.2,0.12 and 0.3?

A.) 0.13
B.) 0.18
C.) 0.8
D.) 0.15

Formula = Fourth propotional = (b × c)/a
A = 0.2 , B = 0.12 and C = 0.3
(0.12 × 0.3)/0.2
0.036/0.2 = 0.18

5.

If a:b=1:2 and b:c=3:4 find a:b:c?

A.) 3:8:6
B.) 3:12:6
C.) 3:6:8
D.) 1:2:4

a:b = 1:2, b:c = 3:4
1:2
3:4
(a = 1 × 3 = 3, b = 2 × 3 = 6 and c = 2 × 4 = 8)
(a = a × b, b = b × b and c = b × c)
a:b:c = 3:6:8

6.

If a:b=1:2, b:c=3:4 and c:d = 2:3 find a:b:c:d?

A.) 3:6:8:24
B.) 6:12:16:24
C.) 6:18:24:16
D.) 3:6:2:3

a:b = 1:2, b:c = 3:4, c:d = 2:3
1:2
3:4
( a = 1 × 3 = 3, b = 2 × 3 = 6 and c = 2 × 4 = 8)
(a = a × b, b= b × b and c= b × c)
a:b:c = 3:6:8
a:b:c = 3:6:8 and c:d = 2:3
(Note: First a,b,c multiplication with c means 2 and last c means 8
multiplication with d means 3
a:b:c:d = 6:12:16:24

7.

If a:b=2:3, b:c=4:5 and c:d=4:2 find a:b:c:d?

A.) 32:48:8:24
B.) 8:12:60:24
C.) 32:18:24:30
D.) 32:48:60:30

a:b = 2:3, b:c = 4:5, c:d = 4:2
2:3
4:5
( a = 2× 4 = 8, b = 37 × 4 = 12 and c = 3 × 5 = 15)
(a = a × b, b = b × b and c = b × c)
a:b:c = 8:12:15
a:b:c = 8:12:15 and c:d = 4:2
(Note: First a=8,b=12,c=15 multiplication with c means 4 and last c = 15
multiplication with d means 2
a:b:c:d = 32:48:60:30

8.

If  2a=6b and 9b=7c, Find a:b:c?

A.) 42:18:14
B.) 3:9:7
C.) 9:27:22
D.) 21:7:9

(2a = 6b => a/b = 6/2)
and (9b = 7c => b/c = 7/9)
=> a:b = 6:2 and b:c = 7:9
a:b:c = 42:14:18 = 21:7:9

9.

If 0.4:1.4 :: 1:4:x, then x=?

A.) 49
B.) 4.9
C.) 0.49
D.) 0.4

0.4 × x = 1.4 × 1.4
x = 1.4 × 1.4/0.4 = 14/10 × 14/10 × 1/(4/10)
14/10 × 14/10 × 10/4
7/10 × 7 = 49/10 = 4.9

10.

If x:y=5:3 then (8x-5y) : (8x+5y)=?

A.) 5:13
B.) 13:5
C.) 5:11
D.) 11:5

x/y = 5/3 (Given)
(8x − 5y)/(8x + 5y)
8(x/y) − 5/8(x/y)+5
( on dividing Nr and Dr by y)
(8(5/3) − 5)/(8(5/3) + 5)
(40/3 − 5/1)/(40/3 + 5/1)
[(40 − 15)/3]/[(40 + 15)/3]
25/55 = 5/11
(8x-5y):(8x+5y) = 5:11

11.

A fraction bears the same ratio to 1/27 as 3/7 does to 5/9. The fraction is?

A.) 7/45
B.) 1/35
C.) 45/7
D.) 5/21

Let the fraction be x. Then,
x:1/27 = 3/7 : 5/9
x × 5/9 = 1/27 × 3/7
x × 5/9 = 1/9 × 1/7
x × 5/9 = 1/63
x × 5 = 9/63
5x = 1/7 = 1/35

12.

The ratio of two numbers is 3:4 and their sum is 28. The greater of the two numbers is?

A.) 8
B.) 12
C.) 14
D.) 16

3:4
Total parts = 7
= 7 parts --> 28 (7 × 4 = 28)
= 1 part ----> 4 (1 × 4 = 4)
= The greater of the two number is = 4
= 4 parts ----> 16 (4 × 4 = 16)

13.

The ratio of three numbers is 5:3:4 and their sum is 108. The second number of the three numbers is?

A.) 12
B.) 27
C.) 15
D.) 29

5:3:4
Total parts = 12
12 parts --> 108
1 part ---->9
The second number of the three numbers is = 3
3 parts ----> 27

14.

Three numbers are in the ratio 3:5:7. The largest number value is 42. Find difference between Smallest & largest number is?

A.) 16
B.) 8
C.) 12
D.) 24

= 3:5:7
Total parts = 15
= The largest number value is 42
= The largest number is = 7
= Then 7 parts -----> 42 ( 7 × 6 = 42 )
= smallest number = 3 & Largest number = 7
= Difference between smallest number & largest number is = 7 - 3 = 4
= Then 4 parts -----> 24 (4 × 6 = 24)

15.

If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?

A.) 10
B.) 20
C.) 30
D.) 40

2:3
2x + 10 : 3x + 10 = 3 : 4
4[2x + 10] = 3[3x + 10]
8x + 40 = 9x + 30
9x - 8x = 40 - 30
x = 10
Then smallest number is = 2
2x = 20
Short cut method:
a:b = 2:3
c:d = 3:4
1.Cross multiplication with both ratios a × d ~ b × c = 2 * 4 ~ 3 × 3 = 8 ~ 9 = 1
2. If 10 is added both the number means 10 × 3 = 30 and 10 × 4 = 40,
Then 30 ~ 40 = 10
=> 1 ---> 10
=> 2 ---> 20

16.

If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 5:7 then find the largest number?

A.) 30
B.) 10
C.) 60
D.) 40

2:3
2x + 10 : 3x + 10 = 5 : 7
7[2x + 10] = 5[3x + 10]
14x + 70 = 15x + 50
15x - 14x = 70 - 50
x = 20
Then the first number is = 2
2x = 40
Short cut method:
a:b = 2:3
c:d = 5:7
1.Cross multiplication with both ratios a × d ~ b × c = 2 × 7 ~ 3 × 5 = 14 ~ 15 = 1
2. If 10 is added both the number means 10 × 5 = 50 and 10 × 7 = 70,
Then 50 ~ 70 = 20
==> 1 ---> 20
==> 2 ---> 40 (Answer is = 40)

17.

If two numbers are in the ratio 5:3. If 10 is Reduced to both of the numbers then the ratio becomes 2:1 then find the smallest number?

A.) 10
B.) 20
C.) 30
D.) 40

5:3
5x - 10 : 3x - 10 = 2 : 1
1[5x - 10] = 2[3x - 10]
5x - 10 = 6x - 20
6x - 5x = 20 - 10
x = 10
the small number is = 3
3x = 30 (Answer = 30)
Short cut method:
a:b = 5:3
c:d = 2:1
1.Cross multiplication with both ratios a × d ~ b × c = 5 × 1 ~ 3 × 2 = 5 ~ 6 = 1
2. If 10 is reduced both the number means 10 × 2 = 20 and 10 × 1 = 10,
Then 20 ~ 10 = 10
=> 1 ---> 10
=> 3 ---> 30 (Answer is = 30)

18.

A mixture contains milk and water in the ratio 5:2. On adding 10 liters of water, the ratio of milk to water becomes 5:3. The quantity of milk in the original mixture is?

A.) 70
B.) 50
C.) 30
D.) 40

milk:water = 5:2
5x : 2x + 10 = 5 : 3
3[5x] = 5[2x + 10]
15x = 10x + 50
15x - 10x = 50
x = 10
The quantity of milk in the original mixture is = 5 : 2 = 5 + 2 = 7
7x = 70
Short cut method:
milk:water = 5 :2
after adding 10 liters of water
milk:water = 5 :3
milk is same but water increse 10liters then the water ratio is increse 1 parts
1 part ---> 10 liters
The quantity of milk in the original mixture is = 5 : 2 = 5 + 2 = 7
7 parts ---> 70 liters  (Answer is = 70)
Short cut method - 2 : for Only milk problems
milk : water
5 : 2
5 : 3
milk ratio same but water ratio 1 part incress per 10 liters
1 part of ratio ---> 10 liters
7 part of ratio ---> 70 liters

19.

A mixture contains milk and water in the ratio 7:3. On adding 20 liters of water, the ratio of milk to water becomes 7:5. Total quantity of milk & water before adding water to it?

A.) 10
B.) 100
C.) 70
D.) 30

milk:water = 7:3
7x : 3x + 20 = 7 : 5
5[7x] = 7[3x + 20]
35x = 21x + 140
35x - 21x = 140
14x = 140
x = 10
The quantity of milk in the original mixture is = 7 : 3 = 7 + 3 = 10
10x = 100
Short cut method:
milk:water = 7 : 3
after adding 20 liters of water
milk:water = 7 : 5
milk is same but water increse 20liters then the water ratio is increse 2 parts
1 part ---> 10 liters
The quantity of milk in the original mixture is = 7 : 3 = 7 + 3 = 10
10 parts ---> 100 liters  (Answer is = 100)
Short cut method - 2 : for Only milk problems
milk : water
7 : 3
7 : 5
milk ratio same but water ratio 2 parts incress per 20 liters
2 part of ratio ---> 20 liters
1 part of ratio ---> 10 liters
10 part of ratio ---> 100 liters

20.

A mixture contains milk and water in the ratio 3:2. On adding 10 liters of water, the ratio of milk to water becomes 2:3. Total quantity of milk & water before adding water to it?

A.) 10
B.) 50
C.) 20
D.) 40

milk:water = 3:2
after adding 10 liters of water
milk:water = 2:3
Olny water patrs increase when mixture of water
milk:wate = 3:2 = 2*(3:2) = 6:4
after adding 10 liters of water
milk:water = 2:3 = 3*(2:3) = 6:9
milk parts always same
Short cut method:
milk:water = 6 : 4
after adding 10 liters of water
milk:water = 6 : 9
milk is same but water increse 10liters then the water ratio is increse 5 parts
5 part ---> 10 liters
The quantity of milk in the original mixture is = 6 : 4 = 6 + 4 = 10
10 parts ---> 20 liters  (Answer is = 20)
Short cut method - 2 : for Only milk problems
milk : water
6 : 4
6 : 9
milk ratio same but water ratio 5 parts incress per 10 liters
5 part of ratio ----> 10 liters
10 part of ratio ---> 20 liters