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

41.

In a mixture 60 litres, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then the quantity of water to be further added is:

   A.) 20 litres
   B.) 30 litres
   C.) 40 litres
   D.) 60 litres

Answer: Option 'D'

Quantity of milk = ( 60x2/3) litres = 40 litres
Quantity of water in it = (60- 40) litres = 20 litres.
New ratio = 1 : 2
Let quantity of water to be added further be x litres.
Then, milk : water = (40/ 20 + x )
Now, (40/20 + x = 80 ) => x = 60
Therefore Quantity of water to be added = 60 litres.

42.

Seats for Mathematics, Physics and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50% and 75% respectively. What will be the ratio of increased seats?

   A.) (2: 3: 4)
   B.) (6: 7 : 8)
   C.) (6 : 8: 9)
   D.) (2 : 3 : 2 )

Answer: Option 'A'

Originally, let the number of seats for Mathematics, Physics and Biology be 5x, 7x and 8x respectively.
Number of increased seats are (140% of 5x), (150% of 7x) and (175% of 8x).
=> (140 / 100 x 5x) , (150 /100 x 7x ) and (175 / 100 x 8x )
=> 7x , 21x/2 and 14x .
Therefore, ratio ofincreased seats
= 7x : (21x/2) : 14x
= 14x : 21x: 28x
=2 : 3 : 4.

43.

A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share? 

   A.) Rs. 500
   B.) Rs. 1500
   C.) Rs. 2000
   D.) Rs. 1200

Answer: Option 'C'

Let the shares of A, Band D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.
Then, 4x - 3x = 1000
=> x = 1000 
Therefore B's share
= Rs. 2x
= Rs. (2 x 1000)
= Rs. 2000.

44.

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

   A.) 4:05
   B.) 2:05
   C.) 6:07
   D.) 3:05

Answer: Option 'A'

Let the third number be x.
Then, first number = 120% of x
= 120x / 100
= 6 x / 5
Second number 
= 150% of x
= 150 x / 100
= 3x / 2
Therefore, Ratio of first two numbers 
= (6x /5 : 3x / 2 )
= 12x : 15x
= 4:5

45.

The ratio of the number of boys and girls at a party was 1:2 but when 2 boys and 2 girls left,the ratio became 1:3. Then the number of persons initially in the party was:

   A.) 24
   B.) 12
   C.) 16
   D.) 25

Answer: Option 'B'

12

46.

The ratio of the number of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls be 20% and 10% respectively, what will be the new ratio? 

   A.) 21:22
   B.) 8:09
   C.) 17:18
   D.) 8:11

Answer: Option 'A'

Originally, let the number of boys and girls in the college be 7x and 8x respectively.
Their increased number is (120% of 7x) and (110% of 8x)
=> (120 / 100 x 7x ) and (110/ 100 x 8x )
=> 42x / 5 and 44x / 5
Therefore, The required ratio = ( 42 x/5 : 44x /5 ) = 42 : 44 = 21 : 22

47.

Salaries of Ravi and Sumit are in the ratio 2 : 3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40 : 57. What is Sumit's salary? 

   A.) Rs. 38,000
   B.) Rs. 20,000
   C.) Rs. 17,000
   D.) Rs. 25,500

Answer: Option 'A'

Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.
Then, (2x+ 4000) / (3x + 4000) = 40 / 57
=> 57(2x + 4000) = 40(3x + 4000)
=> 6x = 68,000
=> 3x = 34,000
Sumit's present salary = (3x + 4000)
= Rs.(34000 + 4000)
= Rs. 38,000.

48.

The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is: 

   A.) 38
   B.) 42
   C.) 30
   D.) 28

Answer: Option 'C'

Let the three numbers be A, B, C.
Then, A : B = 2 : 3 and
B : C = 5 : 8
Now, A : B = 2 : 3
=> A : B = (2 × 5) : (3 × 5) = 10 : 15
Now, B : C = 5 : 8
=> B : C = (5 × 3) : (8 × 3) = 15 : 24
Thus, A : B : C = 10 : 15 : 24
=> A = 10x, B = 15x, C = 24x
Given, A + B + C = 98
=> 10x + 15x + 24x = 98
=> 49x = 98
=> x = 2
Thus, Second number, B = 15x = 15 × 2 = 30

49.

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

50.

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

51.

In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is Rs. 30 in all, how many 5 p coins are there?

   A.) 50
   B.) 150
   C.) 100
   D.) 200

Answer: Option 'B'

Let the number of 25 p, 10 p and 5 p coins be x, 2x, 3x respectively.
Then, sum of their values = Rs. ( 25 x / 100 + 10 x 2x / 100 + 5 x 3x/ 100 ) = RS. 60x /100
Therefore, 60x/100 = 30 <=> x = 30 x 100/60 = 50
Hence, the number of 5 p coins = (3 x 50) = 150.

52.

The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries?

   A.) 23: 33 : 60
   B.) 23: 44 : 60
   C.) 23: 33 : 70
   D.) 43: 33 : 60

Answer: Option 'A'

Let A = 2k, B = 3k and C = 5k.
A's new salary = 115/100 of 2k = (115/200 x 2k) = 23k/10
B's new salary = 100/100 of 3k = ( 110/100 x 3k ) = 33k /10
C's new salary = 120/100 of 5k = (120 /100 x 5k ) = 6k
Therefore, New ratio ( 23k /10 : 33k/10 : 6k ) = 23: 33 : 60

53.

Two number are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is: 

   A.) 33
   B.) 35
   C.) 39
   D.) 43

Answer: Option 'A'

Let the numbers be 3x and 5x.
Then, 3x - 9 / 5x - 9 = 12/3
=> 23×( 3x-9) = 12× (5x - 9)
=> 69x - 207 = 60 x - 108
=> 9x = 99
=> x = 11
Therefore, The smaller number
= (3 x 11)
= 33.

54.

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

55.

 If 0.75 : x :: 5 : 8, then x is equal to :

   A.) 1.12
   B.) 1.2
   C.) 1.25
   D.) 1.3

Answer: Option 'B'

(x x 5) = (0.75 x 8) x = (6/5) = 1.20

56.

The fourth proportional to 5, 8, 15 is:

   A.) 24
   B.) 20
   C.) 18
   D.) 16

Answer: Option 'A'

Let the fourth proportional to 5, 8, 15 be x.
Then, 5 : 8 : 15 : x => 5x = (8 x 15) x (8x 15 ) / 5 = 24

57.

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)

58.

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.) 240
   C.) 360
   D.) 480

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

59.

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

60.

A total amount of Rs. 1800 is to be divided among A,B and C in such a way that half of A’s part, one third of B’s part and one fourth of C’s part is equal. Then A’s part is :

   A.) Rs.400
   B.) Rs.600
   C.) Rs.800
   D.) Rs.900

Answer: Option 'A'

Given, A + B +C = 1800 ----> (1)
(1/2) A = (1/3) B = (1/4) C
=> B = (3/2) A -----> (2)
and C = (4/2) A -----> (3)
Substitute (2) and (3) in (1) => A + (3/2)A + (4/2)A = 1800
=> (2A + 3A + 4A) / 2 = 1800
=> 9A = 1800 × 2
=> A = 200 × 2
=> A = 400


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