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

Answer: (a)

First number = ${3x}/2$

and second number = ${8x}/3$

According to the question,

${{3x}/2 + 15}/{{8x}/3 + 15}= {5/3}/{5/2}$

${{3x+ 30}/2}/{{8x + 45}/3} = 5/3 × 2/5 = 2/3$

${(3x + 30)× 3}/{(8x + 45) × 2} = 2/3$

32x + 180 = 27x + 270

32x - 27x = 270 - 180

5x = 90

$x = 90/5$ = 18

Larger number = ${8x}/3$

= ${8 × 18}/3$ = 48

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: (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)

$x/y = 3/4$

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

= ${4 × 3/4 - 1}/{2× 3/4+ 3}$

= $2/{3/2+ 3} = {2× 2}/9 = 4 : 9$

Answer: (c)

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

= $(1/2 ×12) : (2/3 × 12) : (3/4 × 12)$

= 6 : 8 : 9

Sum of the terms of ratio

= 6 + 8 + 9 = 23

First part

= Rs.$(6/23 × 782)$ = Rs.204