type 1 basic concepts of ratio & proportion Practice Questions Answers Test with Solutions & More Shortcuts

Question : 21 [SSC CGL Prelim 2000]

The fourth proportional to 0.12, 0.21, 8 is :

a) 14

b) 17

c) 56

d) 8.9

Answer: (a)

Let the fourth proportional be x

Then, ${0.12}/{0.21} = 8/x$

or $x =8 ×{0.21}/{0.12}$

or $x =8 × 21/12$

or x = 14

Using Rule 16
Fourth Proportional - Let x be the fourth proportional of a, b and c, then a:b::c:x (Real condition)
$a/b=c/x ⇒ ax=bc$
$x={bc}/a$
Fourth proportional of a, b and c =${bc}/a$

Fourth proportion = ${bc}/a$

= ${0.21 ×18}/{0.12}$= 14

Question : 22 [SSC CGL Prelim 2005]

If x : y = 3 : 2, then the ratio $2x^2 + 3y^2 : 3x^2 - 2y^2$ is equal to :

a) 30 : 19

b) 5 : 3

c) 6 : 5

d) 12 : 5

Answer: (a)

x : y = 3 : 2

$x^2 : y^2$ = 9 : 4

${2x^2 + 3y^2}/{3x^2 - 2y^2} ={2{x^2/y^2}+ 3}/{3{x^2/y^2} - 2}$

= ${2 ×{9/4} +3}/{3× 9/4- 2}={{18 + 12}/4}/{{27 - 8}/4}$

= 30 : 19

Question : 23 [SSC CGL Prelim 2007]

The ratio of A to B is 4 : 5 and that of B to C is 2 : 3. If A equals 800, C equals

a) 1500

b) 2000

c) 1200

d) 1000

Answer: (a)

A : B = 4 : 5

B : C = 2 : 3

A : B : C = 4 × 2 : 5 × 2 : 5 × 3

= 8 : 10 : 15

If A equals 800, then C equals 1500.

Question : 24 [SSC CGL Prelim 2003]

If a : b = $2/9: 1/3, b : c = 2/7 : 5/14 and d : c = 7/10 : 3/5$ then a : b : c : d is

a) 8 : 12 : 15 : 7

b) 30 : 35 : 24 : 16

c) 16 : 24 : 30 : 35

d) 4 : 6 : 7 : 9

Answer: (c)

Using Rule 19 (ii),

a : b = $2/9 : 1/3$ = 2 : 3

b : c = $2/7 :5/14$ = 4 : 5

d : c = $7/10: 3/5$ = 7 : 6

c : d = 6 : 7

Thus,

a : b=2 : 3
b : c=         4 : 5
c : d=                  6 : 7
a : b : c : d=2×4×6 : 3×4×6 :
3×5×6 : 3×5×7

= 16 : 24 : 30 : 35

Question : 25 [SSC CGL Prelim 2005]

If A : B : C = 2 : 3 : 4, then ratio $A/B : B/C : C/A$ is equal to

a) 8 : 9 : 24

b) 4 : 9 : 16

c) 8 : 9 : 12

d) 8 : 9 : 16

Answer: (a)

A : B : C = 2 : 3 : 4

$A/B = 2/3, B/C = 3/4, C/A= 4/2 = 2$

$A/B : B/C : C/A = 2/3 : 3/4 : 2/1$

= 8 : 9 : 24

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