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

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

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: (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)

a : (b+c) = 1: 3

${b+ c}/a = 3/1 ⇒ {b+c}/a+1 =3/1$+1

${a+ b + c}/a= {3+1}/1 = 4/1$ ... (i)

Similarly, ${a + b}/c = 7/5$

${a + b + c}/c = 12/5$ ... (ii)

On dividing (i) by (ii),

$c/a = {4 × 5}/12 = 5/3$ =k ... (iii)

From equation (i), b = 4k

$b/{a + c} = {4k}/{3k + 5k} =1 : 2$

Answer: (c)

We can write a : c by compounding a : b and b : c

$a/c = a/b × b/c, a/c = 3/4 × 8/9, a/c =2/3$

a : c = 2 : 3

A : C = xp : yq

= 3 × 8 : 4 × 9 = 2 : 3

Answer: (c)

Mean proportional

=$√{(3+√2)(12-√{32})}$

= $√{(3+√2)4(3-√2)}$

= 2$√{9 - 2} = 2√7$