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

Answer: (c)

Given, $x/y = 2/3$ ... (i)

Expression = ${3x + 2y}/{9x + 5y}$

= ${3x/y + 2}/{9x/y+ 5} = {3×2/3+2}/{9×2/3+5}$[from (i)]

= ${2 + 2}/11 =4/11$

Answer: (c)

Mean proportional

=$√{(3+√2)(12-√{32})}$

= $√{(3+√2)4(3-√2)}$

= 2$√{9 - 2} = 2√7$

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: (a)

$m/n = 3/2$ (Given)

${4m+ 5n}/{4m- 5n}={4(m/n)+ 5}/{4(m/n)- 5}$

= ${4 ×3/2 +5}/{4× 3/2- 5}={6 +5}/{6- 5}$ = 11: 1

Answer: (a)

If $a/b = c/d = e/f$, then each of these ratios is equal to ${a+c+e}/{b+d+ f}$

Here, $p/q =r/s= t/u = 2/3$

${mp}/{mq}= {nr}/{ns}= {ot}/{ou} = 2/3$

${mp +nr+ ot}/{mq+ ns+ ou}= 2/3$ or 2 : 3

Answer: (d)

First part = x and second part

= 94 - x

${x/5}/{{94 - x}/8} = 3/4$

$x/5 × 8/(94 - x) =3/4$

32 x = 15 × 94 - 15x

47 x = 15 × 94

$x = {15 × 94}/47$ = 30