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

1.

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

2.

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

Answer: Option 'B'

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 

3.

For every 2 chocolate Ram gets Shyam is given 3 chocolate. If the total number of chocolate distributed to them is 65, then find the number of chocolates Shyam received.

   A.) 30
   B.) 39
   C.) 34
   D.) 45

Answer: Option 'B'

39

4.

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

5.

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. 2000
   B.) Rs. 2500
   C.) Rs. 1500
   D.) Rs. 1000

Answer: Option 'A'

Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.
Then, if C gets Rs. 1000 more than D
=> 4x - 3x = 1000
=> x = 1000
B's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000
Answer is 2000

6.

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.) 39
   D.) 13

Answer: Option 'B'

Given, a/b = 1/2 and (a+7)/(b+7) = 3/5 => a = 14 and b = 28

7.

If Rs.800/- Rupees are divided among a,b and c in such a way that A’s share 4 times more than B, B’s share is 3 times more than C. The C’s share is? 

   A.) Rs.650/-
   B.) Rs.600/-
   C.) Rs.150/-
   D.) Rs.50/-

Answer: Option 'D'

A:B:C = 12:3:1 
Total parts = 16 
C's share is = 1 parts 
16 -----> Rs.800/- 
1 -----> Rs.50/- (Answer = Rs.50/-)

8.

Rs.630/- distributed among A,B and C such that on decreasing their shares by RS.10,RS.5 and RS.15 respectively, The balance money would be divided among them in the ratio 3:4:5. Then, A’s share is:? 

   A.) Rs.150/-
   B.) Rs.200/-
   C.) Rs.160/-
   D.) Rs.255/-

Answer: Option 'C'

A:B:C = 3:4:5 
Total parts = 12 
A's share is = 3 parts 
12 -----> Rs.600/- 
3 -----> Rs.150/- 
A's total = 150 + 10 = Rs.160/-

9.

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

Answer: Option 'B'

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

10.

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.) 15 and 20
   B.) 16 and 24
   C.) 13 and 17
   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

11.

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

12.

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.) 220
   B.) 120
   C.) 240
   D.) 90

Answer: Option 'B'

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

13.

Rs.4800/- are divided among P,Q and R in such a way that the share of P is 5/11 of the combined share of Q and R. Thus, P gets:? 

   A.) Rs.300/-
   B.) Rs.3300/-
   C.) Rs.1800/-
   D.) Rs.1500/-

Answer: Option 'D'

P/(Q+R) = 5/11 
16 ----> Rs.4800/-
1 -----> Rs.300/-
P = 5 parts 
5 ------> Rs.1500/- P = 300 × 5 = Rs.1500/- 

14.

The ages of Manoj and Amit are in the ratio 2:3. After 12 years, their ages will be in the ratio 11:15. The age of Amit is: 

   A.) 48 years
   B.) 56 years
   C.) 40 years
   D.) 32 years

Answer: Option 'A'

Given the present age ratio of Manoj and Amit = 2 : 3
=> present age of Manoj = 2x
present age of Amit = 3x
Given after 12years, their ages will be in the ratio 11:15.
thus, after 12 years the age of Manoj will be = 2x + 12
and the age of Amit will be= 3x + 12
=> (age of Manoj after 12 years / age of Amitafter 12 years) = 11 / 15
=> (2x + 12) / (3x + 12) = 11 / 15
=> 15(2x + 12) = 11(3x + 12)
=> 30x + 180 = 33x + 132
=>33x - 30x = 180 - 132
=> 3x = 48
Thus,present age of Amit = 3x = 48 years.

15.

A bag contains one rupee, 50 paise and 25 paise coins in the ratio 5:7:9. If the total amount in the bag is Rs. 430, find the number of coins of 25 paise

   A.) 200
   B.) 300
   C.) 360
   D.) 420

Answer: Option 'C'

360

16.

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

17.

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

Answer: Option 'D'

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)

18.

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

Answer: Option 'C'

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.

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

Answer: Option 'B'

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.

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

Answer: Option 'C'

Let Numbers be m and n,
m/n = 2/3
Adding 8 on both sides,we get
=> (m+8) / (n+8) = 3 / 4
=> 4m + 32 = 3n + 24
By solving each of them seperately we get the value of m , n
=> 4m + 32 =0
=> 4m = 32
=> m = 32 / 4
=> m = 8
3n + 24 = 0
=> 3n = 24
=> n = 24 / 3
=> n = 8
So according to the given ratios,
The numbers are in 2 : 3
m = 8 × 2 = 16
n = 8 × 3 = 24
So m =16 , n = 24


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