Ratios and Proportions (114 Questions with Explanation)

46.

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

47.

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.

48.

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

Answer: Option 'A'

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

49.

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

50.

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

Answer: Option 'D'

(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

51.

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

Answer: Option 'A'

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

52.

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

53.

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

54.

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

55.

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)

56.

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

57.

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) 

58.

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

59.

If 0.4:1.4 :: 1:4:x, then x=?

   A.) 49
   B.) 4.9
   C.) 0.49
   D.) 0.4

Answer: Option 'B'

0.4 × x = 1.4 × 1.4 
x = 1.4 × 1.4/0.4 = 14/10 × 14/10 × 1/(4/10) 
14/10 × 14/10 × 10/4 
7/10 × 7 = 49/10 = 4.9

60.

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/-)

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