Ratios and Proportions (114 Questions with Explanation)

1.

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

Answer: Option 'B'

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

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 numbers are in the ratio 11:12, if 14 is added to each they are in the ratio 69:74. Find the two numbers.

   A.) 55 and 60
   B.) 55 and 120
   C.) 63 and 74
   D.) 88 : 97

Answer: Option 'A'

Numbers are in the ratio 11 : 12 
Two numbers are 11k and 12k 
Adding 14 to both the numbers, 11k+14 and 12k+14 
Given that 11k+14 : 12k+14 = 69 : 74 => 74(11k+14) = 69(12k+14) => (814-828)k = 14 x (-5) => k = 5 
First Number, 11 x k = 55 Second Number 12 x k = 60 
Numbers are 55 and 60

4.

If Rs.1440/- are divided among A,B and C so that A receives 1/3rd as much as B and B receives 1/4th as much as C. The amount B received is: 

   A.) Rs.90/-
   B.) Rs.270/-
   C.) Rs.1080/-
   D.) Rs.27/-

Answer: Option 'B'

A:B:C = 1:3:12 
Total parts = 16 
B's share is = 3 parts 
16 -----> 1440 
1 -----> 90 
3 -----> 270 (B's share is 270) 

5.

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

Answer: Option 'D'

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)

6.

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

7.

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

8.

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

Answer: Option 'D'

= 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) 

9.

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

10.

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)

11.

If x:y=5:3 then (8x-5y) : (8x+5y)=? 

   A.) 5:13
   B.) 13:5
   C.) 5:11
   D.) 11:5

Answer: Option 'C'

x/y = 5/3 (Given) 
(8x − 5y)/(8x + 5y) 
8(x/y) − 5/8(x/y)+5 
( on dividing Nr and Dr by y) 
(8(5/3) − 5)/(8(5/3) + 5) 
(40/3 − 5/1)/(40/3 + 5/1) 
[(40 − 15)/3]/[(40 + 15)/3] 
25/55 = 5/11 
(8x-5y):(8x+5y) = 5:11 

12.

Find the third proportional to 9 and 12? 

   A.) 9
   B.) 108
   C.) 16
   D.) 9

Answer: Option 'C'

Formula = Third proportional = (b × b)/a 
A = 9 and B = 12 
(12 × 12)/ 9 = 144/9 = 16

13.

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

14.

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/-)

15.

A mixture contains milk and water in the ratio 5:2. On adding 10 liters of water, the ratio of milk to water becomes 5:3. The quantity of milk in the original mixture is?

   A.) 70
   B.) 50
   C.) 30
   D.) 40

Answer: Option 'A'

milk:water = 5:2 
5x : 2x + 10 = 5 : 3 
3[5x] = 5[2x + 10] 
15x = 10x + 50 
15x - 10x = 50 
x = 10 
The quantity of milk in the original mixture is = 5 : 2 = 5 + 2 = 7 
7x = 70 
Short cut method: 
milk:water = 5 :2  
after adding 10 liters of water 
milk:water = 5 :3  
milk is same but water increse 10liters then the water ratio is increse 1 parts  
1 part ---> 10 liters  
The quantity of milk in the original mixture is = 5 : 2 = 5 + 2 = 7 
7 parts ---> 70 liters  (Answer is = 70) 
Short cut method - 2 : for Only milk problems 
milk : water 
5 : 2 
5 : 3 
milk ratio same but water ratio 1 part incress per 10 liters 
1 part of ratio ---> 10 liters 
7 part of ratio ---> 70 liters

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