type 6 fractions based ratio & proportion problems Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (b)

x : y = 3 : 4 = 9 : 12

y : z = 3 : 4 = 12 : 16

x : y : z = 9 : 12 : 16

${x + y + z}/{3z} - {9k +12k +16k}/{3 × 16k} = 37/48$

Answer: (b)

Ratio of division

= $1/2 : 2/3 : 4/5$

= $1/2 × 30 : 2/3 × 30 : 4/5$ × 30

[LCM of 2, 3 and 5 = 30]

= 15 : 20 : 24

Sum of the terms of ratio

= 15 + 20 + 24 = 59

Second part

= Rs.$(20/59 × 177)$ = Rs.60

Answer: (c)

Let the number to be added be z.

${x +z}/{y +z} = p/q$

qx + zq = py + zp

zp - zq = qx - py

z (p - q) = qx - py

z =${qx - py}/{p - q}$

Answer: (b)

$x/y = 3/4$ (Given)

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

(Dividing numerator and denominator by y)

= ${2x/y+3}/{3 - 2 x/y} = {2× 3/4+3}/{3-2× 3/4}$

= ${3/2 + 3}/{3 - 3/2}$

= ${3 + 6}/{6 - 3}= 9/3$ = 3 : 1

Answer: (d)

According to the question,

${5A}/19 = {2B}/5$

$5A = {19 × 2B}/5$

A = ${38 × B}/{5× 5}$

A : B = 38 : 25

Sum of the terms of ratio

= 38 + 25 = 63

B’s share = Rs.$(25/63 × 6300)$

= Rs.2500

Answer: (d)

$x/y = 3/4$

${4x - y}/{2x +3y} ={4x/y-1}/{2x/y+3}$

= ${4 × 3/4 - 1}/{2× 3/4+ 3}$

= $2/{3/2+ 3} = {2× 2}/9 = 4 : 9$