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

1.

Rs. 770 have been divided among A, B and C such that A receives two-ninths of what B and C together receive. Then A's share is 

   A.) Rs. 165
   B.) Rs. 140
   C.) Rs. 154
   D.) Rs. 170

Answer: Option 'B'

A = (2/9) (B+C) A + B + C = 770 (Given)
-----> A + 9A/2 = 770 => 11A = 770 x 2 => A = 70 x 2 = 140

2.

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

Answer: Option 'C'

Dozen means = 12 
12/(2+3) = 12/5 ==> wrong 
12/(3+4) = 12/7 ==> wrong 
12/(5+7) = 12/12 = 1 ==> Right (Answer = 5:7)

3.

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 

4.

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

5.

If a:b=1:2 and b:c=3:4 find a:b:c? 

   A.) 3:8:6
   B.) 3:12:6
   C.) 3:6:8
   D.) 1:2:4

Answer: Option 'C'

a:b = 1:2, b:c = 3:4 
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 

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.) 24
   C.) 28
   D.) 32

Answer: Option 'C'

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

7.

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

8.

The fourth proportional to 5, 8, 25 is ________

   A.) 40
   B.) 45
   C.) 55
   D.) 35

Answer: Option 'A'

Given
Let the fourth proportional to 5, 8, 25 be x.
Then, 5 : 8 : 25 : x
=> 5x = (8 x 25)
=> x = (8 x 25)/5
= 40

9.

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.

10.

Rs. 770 have been divided among A, B and C such that A receives two-ninths of what B and C together receive. Then A's share is 

   A.) Rs. 165
   B.) Rs. 140
   C.) Rs. 154
   D.) Rs. 170

Answer: Option 'B'

Given, A = (2/9) (B+C) ==>B+C = 9A / 2
and also given, A + B + C = 770
Subs,B+C = 9A / 2 in the above equation
=> A + 9A/2 = 770
=> 11A = 770 x 2
=> A = 70 x 2
=> A =140

11.

If a/b = 3 / 2 then find (3a + b ) / (3a - b) = 

   A.) 11 / 5
   B.) 11 / 7
   C.) 12 / 7
   D.) 11 / 2

Answer: Option 'B'

11 / 7

12.

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.) 28
   D.) 32

Answer: Option 'C'

Let two numbers be X and Y
Given X/Y = 1/2
2X = Y
If 7 is added to two numbers,
(X+7) / (Y+7) = 3/5
Substitute Y=2X
(X+7) / (2X+7) =3/5
=> 5(X+7) = 3(2X+7)
=> 5X + 35 = 6X + 21
6X - 5X = 35 - 21 => X= 14
The greater number is Y =2X => 2 x 14 =28
Answer is 28

13.

If a:b=8:15, b:c=13:3 and c:d = 4:9 then find a : b : c : d.

   A.) 416 : 780 : 180 : 405
   B.) 416 : 780 : 90 : 405
   C.) 416 : 680 : 180 : 405
   D.) 416 : 780 : 180 : 305

Answer: Option 'A'

Given, a : b = 8 : 15
=> a x 13 : b x 13 =8 x 13 : 15 x 13
=> a : b = 104 : 195 ----> eqn (1)

Given, b : c = 13 : 3
=> b x 15 : c x 15 =13 x 15 : 3x 15
=> b : c = 195 : 45 ----> eqn (2)

From eqn (1) and (2) ---> a : b : c = 104 : 195 : 45

=> a x 4 : b x 4 : c x 4 =104 x 4 : 195 x 4 : 45 x 4
=> a : b : c = 416 : 780 : 180 ----> eqn (3)

Given,c:d = 4:9
=> c x 45 : d x 45 = 4 x 45 : 9 x 45
=> c : d = 180 : 405 ----> eqn (4)

From eqn (3) and (4) ---> a : b : c : d = 416 : 780 : 180 :405

14.

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

Answer: Option 'A'

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.

15.

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

16.

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

17.

If two numbers are in the ratio 2:3. If 10 is added to both of the numbers then the ratio becomes 3:4 then find the smallest number?

   A.) 10
   B.) 20
   C.) 30
   D.) 40

Answer: Option 'B'

2:3 
2x + 10 : 3x + 10 = 3 : 4 
4[2x + 10] = 3[3x + 10] 
8x + 40 = 9x + 30 
9x - 8x = 40 - 30 
x = 10 
Then smallest number is = 2 
2x = 20 
Short cut method: 
a:b = 2:3 
c:d = 3:4 
1.Cross multiplication with both ratios a × d ~ b × c = 2 * 4 ~ 3 × 3 = 8 ~ 9 = 1 
2. If 10 is added both the number means 10 × 3 = 30 and 10 × 4 = 40, 
Then 30 ~ 40 = 10 
=> 1 ---> 10 
=> 2 ---> 20 

18.

The number of candidates writing three different entrance exams is in the ratio 4:5:6. There is a proposal to increase these numbers of candidates by 40%, 60%, and 85%, respectively. What will be the ratio of increased numbers? 

   A.) 56:80:11
   B.) 56:90:111
   C.) 56:60:111
   D.) 56:70:111

Answer: Option 'A'

Given ratio of number of candidates is 4:5:6
Let the number of candidates for 3 exams be 4k, 5k, and 6k, respectively.
After increasingthenumberof candidates by 40%, 60% and 85%, respectively.
=> Number of candidates become (140% of 4k),(160% of 5k),(185% of 6k)
=> (140x4k) /100, (160x5k)/100 and (185x6k) /100
= 56k/10, 80k/10, and 111k/10
Now, the required new ratio is: 56k/10: 80k/10 : 111k/10
56 : 80 : 111

19.

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/-

20.

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'

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