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

41.

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.

42.

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)

43.

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

44.

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

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

45.

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.) 24
C.) 32
D.) 28

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

46.

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)

47.

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

48.

A bag contains 50p,Rs.1/- and Rs2/- coins in the ratio of 4:2:1 respectively. If the total money in the bag is Rs.60/-. Find the number of 50p coins in that bag?

A.) 60 coins
B.) 10 coins
C.) 20 coins
D.) 40 coins

50paisa : Rs.1/- : Rs.2/- = 4 : 2 : 1  ---> coins ratio
= 2 : 2 : 2 ----> money ratio
Rs.2/- × 10 coins = Rs.20/-
Rs.1/- × 20 coins = Rs.20/-
50 Paisa × 40 coins = Rs.20/-
Then 50paisa coins in that bag = 40 cions

49.

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)

50.

Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by

A.) One-ninth
B.) One-eighth
C.) One-seventh
D.) Seven-eighths

Given
When there are 8 people, the share of each person is 1/8
When there are 7 people, the share of each person is 1/7
Increase in the share of each person is
=>1/7 × 1/8
=> 1 / 56
Which if 1/7 of 1/8 of the original share of each person.
Share of each person = 1 / 7.

51.

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

52.

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

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.

20 boys and 25 girls form a group of social workers. During their membership drive, the equal number of boys and girls joined this group. How many members does the group have now, if the ratio of boys to girls is 7 : 8 ?

A.) 65
B.) 75
C.) 80
D.) 85

Let x girls and x boys join this group.
Then (20+x) / (25+x) = 7/8 => 160 + 8x = 175 + 7x => x = 15 Boys = 20 + 15 = 35 Girls = 25 + 15 = 40, total = 35 + 40 = 75

55.

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

56.

Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by

A.) One-seventh
B.) Seven-eighths
C.) One-eighth
D.) One-ninth

When there are 8 people, the share of each person is 1/8
When there are 7 people, the share of each person is 1/7
Increase in the share of each person is 1/7 - 1/8 = 1 / 56 ,
Which is 1/7 of 1/8 of the original share of each person.

57.

Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by

A.) One-ninth
B.) One-seventh
C.) One-eighth
D.) Seven-eighths

When there are 8 people, the share of each person is 1/8 => (Original Share)
When there are 7 people, the share of each person is 1/7
Increase in the share of each person is 1/7 – 1/8 = 1 / 56
1 / 56 ==> Which is 1/7 of 1/8 ==> 1/7 of the original share of each person.

58.

If Rs.540/- are divided among A,B and C in such a way that A’s share is ½nd of B share and B’s share is 1/3rd of C’s share. The share of A is?

A.) Rs.80/-
B.) Rs.360/-
C.) Rs.60/-
D.) Rs.120/-

A:B:C = 1:2:6
Total parts = 9
A's share is = 1 parts
9 -----> Rs.540/-
1 -----> Rs.60/-

59.

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

60.

If a dozen mirrors are fallen down. The ratio between broken and unbroken mirrors is:

A.) 2:3
B.) 3:4
C.) 5:7
D.) 5:4