# 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

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 )

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

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

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

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

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

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

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

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

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

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

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

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

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

(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

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)

(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

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)

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

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