type 1 basic concepts of ratio & proportion Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (b)

$A : D = A/D =A/B ×B/C× C/D$

= $3/4× 5/7× 8/9 =10/21$= 10 : 21

A : D = xpm : yqn

= 3 × 5 × 8 : 4 × 7 × 9

= 10 : 21

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

Fourth proportion = ${bc}/a$

= ${0.21 ×18}/{0.12}$= 14

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

Answer: (b)

Using Rule 33,

$a/b = c/d = e/f = 1/2$

${pa}/{pb} = {qc}/{qd} = {re}/{rf}= 1/2$

${pa +qc+ re}/{pb+ qd+ rf} = 1/2$ or 1 : 2

Answer: (d)

$x/y= 3/1 ⇒ x^3/y^3 =27/1$

${x^3 - y^3}/{x^3 + y^3} = {27- 1}/{27 + 1}$

[By componendo and dividendo]

= $26/28 = 13/14$ = 13 : 14

Answer: (a)

$x = 1/3y$ ⇒ x : y = 1 : 3

Again, $y = 1/2z$ ⇒ y : z

= 1 : 2 = 3 : 6

x : y : z = 1 : 3 : 6