Ratios and Proportions (114 Questions with Explanation)

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1.

Find the fourth proportional to 2.4, 4.6 and 7.6? 

   A.) 14
   B.) 14.657
   C.) 15.56
   D.) 14.56

Answer: Option 'D'

Formula = Fourth propotional = (b × c)/a 
A = 2.4 , B = 4.6 and C = 7.6 
(4.6 × 7.6)/2.4 = 14.56

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2.

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

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3.

Find the mean proportional between 49 & 81? 

   A.) 16
   B.) 10
   C.) 63
   D.) 12

Answer: Option 'C'

Formula = √a×b
A = 49 and B = 81 
√49×81 = 7 × 9 = 63

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4.

Find the fourth proportional to 0.2,0.12 and 0.3? 

   A.) 0.13
   B.) 0.18
   C.) 0.8
   D.) 0.15

Answer: Option 'B'

Formula = Fourth propotional = (b × c)/a 
A = 0.2 , B = 0.12 and C = 0.3 
(0.12 × 0.3)/0.2 
0.036/0.2 = 0.18

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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 

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6.

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 

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7.

If a:b=2:3, b:c=4:5 and c:d=4:2 find a:b:c:d? 

   A.) 32:48:8:24
   B.) 8:12:60:24
   C.) 32:18:24:30
   D.) 32:48:60:30

Answer: Option 'D'

a:b = 2:3, b:c = 4:5, c:d = 4:2
2:3 
4:5 
( a = 2× 4 = 8, b = 37 × 4 = 12 and c = 3 × 5 = 15)
(a = a × b, b = b × b and c = b × c)
a:b:c = 8:12:15 
a:b:c = 8:12:15 and c:d = 4:2
(Note: First a=8,b=12,c=15 multiplication with c means 4 and last c = 15
multiplication with d means 2
a:b:c:d = 32:48:60:30 

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8.

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

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9.

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

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10.

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 

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