## Ratios and Proportions

• 1. Find the fourth proportional to 2.4, 4.6 and 7.6?
A.) 14
B.) 14.657
C.) 15.56
D.) 14.56

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

• 2. Find the third proportional to 9 and 12?
A.) 9
B.) 108
C.) 16
D.) 9

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

• 3. Find the mean proportional between 49 & 81?
A.) 16
B.) 10
C.) 63
D.) 12

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

• 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

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

• 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

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. 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

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

• 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

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

• 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

(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

• 9. If 0.4:1.4 :: 1:4:x, then x=?
A.) 49
B.) 4.9
C.) 0.49
D.) 0.4

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

• 10. If x:y=5:3 then (8x-5y) : (8x+5y)=?
A.) 5:13
B.) 13:5
C.) 5:11
D.) 11:5

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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