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

1.

Ratio between two numbers is 3 : 2 and their difference is 225, then the smaller number is:

   A.) 90
   B.) 450
   C.) 270
   D.) 480

Answer: Option 'B'

Given, the ratio of two numbers = 3 : 2
Let the two numbers be 3x and 2x
Given, their difference = 225
=> 3x - 2x = 225
=> x = 225
Smaller number = 2x = 2 × 225 = 450

2.

One-third of the contents of a container evaporated on the 1st day, three-fourths of the remaining evaporated on the second day. What part of the contents of the container is left at the end of the second day?

   A.) One-fourth
   B.) One-half
   C.) One-eighteenths
   D.) One-sixth

Answer: Option 'D'

After first day, 2/3 rd of the contents remain (i.e., 1 - (1/3) = 2/3)
After second day 2/3 (3/4) x (2/3) = 1/6 of the content remains

3.

If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number? 

   A.) 5:3
   B.) 7:3
   C.) 3:7
   D.) 4:7

Answer: Option 'A'

Let the Two numbers be A, B
40% of A = 2/3 B
Then, 40A /100 = 2B/3
=> 2A/5 = 2B/3
=> A/B = (2/3 x 5/2 ) = 5/3
Therefore, A : B = 5 : 3

4.

Find the mean proportional between 49 & 81? 

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

Answer: Option 'C'

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

5.

A sum of Rs. 53 is divided among A,B,C in such a way that A gets Rs. 7 more than B and B gets Rs. 8 more than C.Then the ratio of their shares is : 

   A.) (10:18:25)
   B.) (18:25:10)
   C.) (25:18:10)
   D.) (25:18:10)

Answer: Option 'C'

Given
Sum = Rs. 53
Suppose C gets Rs. x
Then, B gets Rs. (x + 8) and A gets Rs. (x + 15)
⇒ x + x + 8 + x + 15 = 53
∴ 3 x = 53 - 8 - 15
3 x = 30
x = 30 / 3
x = 10
C = 10
B = ( 10 + 8 ) = Rs 18
C = ( 10 + 15) =Rs 25
So, A : B : C = 25 : 18 : 10

6.

Two numbers are in the ratio 2:3. If eight is added to both the numbers, the ratio becomes 3:4. The numbers are

   A.) 13 and 17
   B.) 16 and 24
   C.) 15 and 20
   D.) 17 and 9

Answer: Option 'B'

Numbers be m and n, m/n = 2/3 (m+8)/(n+8) = ? => m=16 and n= 24

7.

Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is?

   A.) 02:05
   B.) 04:05
   C.) 03:05
   D.) 05:05

Answer: Option 'B'

Let the third number be x.
Then, first number = 120% of x = 1.2x = (6x/5)
Second number = 150% of x = 1.5x =(3x/2)
Ratio of first two numbers = (6x/5) :(3x/2) => (6x/5) x (2/3x) =>(12x) / (15x) = 12/15
= 4/5
Ratio is 4 : 5

8.

Two numbers are in the ratio 7:9. If 12 is subtracted from each of them, the ratio becomes 3:5. The product of the numbers is:

   A.) 567
   B.) 657
   C.) 768
   D.) 1575

Answer: Option 'A'

Given, ratio of two numbers = 7: 9 Let two numbers be 7x and 9x
If 12 is subtracted from each number, => (7x -12) / (9x - 12) = 3/5 => 5(7x - 12) = 3(9x - 12) => 35x - 60 = 27x - 36 => 8x = 24 => x = 3
Product of the numbers = 7x × 9x = 7(3) × 9(3) = 21 × 27 = 567

9.

A bag contains 5p,10p and Rs20p coins in the ratio of 1:2:4 respectively. If the total money in the bag is Rs.84/-. Find the number of 10p coins in that bag? 

   A.) 160 coins
   B.) 20 coins
   C.) 128 coins
   D.) None of these

Answer: Option 'A'

5paisa : 10paisa : 20paisa = 1 : 2 : 4  ---> coins ratio  
= 5 : 20 : 80 ---> money ratio 
5 paisa × 80 coins = Rs.4/- 
10 paisa × 160 coins = Rs.16/- 
Then 10 paisa coins in that bag = 160 cions

10.

The ratio of number of boys and girls in a school of 720 students is 7:5. How many more girls should be admitted to make the ratio 1:1? 

   A.) 120
   B.) 220
   C.) 230
   D.) 121

Answer: Option 'A'

Given, boys : girls = 7 : 5
Let, the total number of boys = 7x and total number of girls= 5x
Given, total students = 720
=> 7x + 5x = 720
=> 12x = 720
=> x = 60
so, total number of boys = 7x = 7 * 60 = 420 and
total number of girls= 5x = 5 * 60 = 300
Let y be the number of girls added to make the ratio 1 : 1
=> 420 / (300 + y) = 1/1
=> 420 = (300 + y)
=> y = 420 - 300
=> y = 120
So, 120 more girls should be admitted to make the ratio 1:1

11.

Two numbers are in the ratio 1:2, if 20 is added to each they are in the ratio 11:18. Find the two numbers.

   A.) 35 and 70
   B.) 25 and 70
   C.) 44 and 72
   D.) 44 and 88

Answer: Option 'A'

Numbers are in the ratio 1 : 2 
Two numbers are 1k and 2k 
Adding 20 to both the numbers, 1k+20 and 2k+20 
Given that 1k+20 : 2k+20 = 11 : 18 => 18(1k+20) = 11(2k+20) => (18-22)k = 20 x (-7) => k = 35 
First Number , 1 x k = 35 Second Number 2 x k = 70 
Numbers are 35 and 70

12.

If A:B = 3:2 B:C= 4:3 then A:B:C=?

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

Answer: Option 'A'

(6:4:3)

13.

Find the fourth proportional to 2.4, 4.6 and 7.6? 

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

Answer: Option 'D'

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

14.

A mixture contains milk and water in the ratio 3:2. If 4 liters of water is added to the mixture, milk and water in the mixture becomes equal. The quantity of milk in the mixture in liter is? 

   A.) 6
   B.) 12
   C.) 24
   D.) 36

Answer: Option 'B'

Given, Milk and Water ratio = 3 : 2
=> quantity of milk= 3x liters
quantity of water = 2x liters
If 4 liters of water is added to the mixture,
New Milk and Water ratio = 1 : 1 (Since equal),
quantity of milk in the new mixture,= 3x liters
quantity of water in the new mixture = 2x + 4 liters.
=>quantity of Milk in new mixture/ quantity of water in new mixture = 1 / 1
=> 3x / (2x + 4) = 1 / 1
=> 3x = (2x + 4)
=> 3x - 2x = 4
=> x = 4
Thus,quantity of milk= 3x liters = 3 × 4 = 12 liters

15.

Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:

   A.) 05:07
   B.) 04:05
   C.) 02:07
   D.) 02:05

Answer: Option 'B'

Let the third number be x.
Then, first number = 120% of x = 1.2x = (6x/5) Second number = 150% of x = 1.5x =(3x/2)
Ratio of first two numbers = (6x/5) : (3x/2) = 12/15 = 4/5
Ratio is 4 : 5

16.

If the ratio of boys to girls in a class is B and the ratio of girls to boys is G, then 3 (B + G) is

   A.) Equal to 3
   B.) Less than 3
   C.) More than 3
   D.) Less than one-third

Answer: Option 'C'

Boys = x, Girls = y x/ y = B and y/x = G 3(B+G) = 3( y/x + x/y = 3 (x2+y2)/xy > 3

17.

If a:b=5:3, b:c=5:4 and c:d = 11:5 then find a:b:c:d

   A.) 275:165:132:50
   B.) 275:155:132:60
   C.) 275:165:132:50
   D.) 275:165:122:60

Answer: Option 'A'

a:b = 5x 5 : 3x 5 = 25 : 15 b:c = 5x 3 : 3x 4 = 15 : 12 a:b:c = 25 : 15 : 12 
a x 11:b x 11:c x 11 = 275 : 165 : 132 
c:d = 11:5 => c x 12 : d x 12 = 132:60 
a:b:c:d = 275:165:132:60

18.

Two vessels of equal volumes contains milk and water mixed in the ratio 1:2,2:3. When These mixtures are mixed to form a new mixture, what is the ratio of milk and water? 

   A.) 11:19
   B.) 19:11
   C.) 2:5
   D.) None of these

Answer: Option 'A'

1:2 , 2:3 
1/3:2/3 , 2/5:3/5 
= 1/3 + 2/5 : 2/3 + 3/5 
= 11/15 : 19/15 = 11 : 19 

19.

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

Answer: Option 'B'

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

20.

Two numbers are in the ratio of 1:2. If 7 be added to both, their ratio changes to 3:5. The greater number is 

   A.) 20
   B.) 28
   C.) 42
   D.) 36

Answer: Option 'B'

Let the two numbers be a, b.
Given, ratio b/w two numbers = 1 : 2
=> a / b = 1 / 2
=> a = x, b = 2x
If 7 be added to both, their ratio changes to 3:5
=> (a+7) / (b+7) = 3 / 5
=> On substituting a = x, b = 2x in the above eqn, we get
=> (x+7) / (2x+7) = 3 / 5
=> 5 (x+7) = 3 (2x+7)
=> 5x + 35 = 6x + 21
=> 6x - 5x = 35 - 21
=> x = 14
Therefore, a = x = 14
b = 2x = 2 * 14 = 28
The greater number is b = 28


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