type 6 fractions based ratio & proportion problems Section-Wise Topic Notes With Detailed Explanation And Example Questions
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The following question based on ratio & proportion topic of quantitative aptitude
(a) 48
(b) 64
(c) 36
(d) 27
The correct answers to the above question in:
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
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Read more fractions based ratio and proportion problems Based Quantitative Aptitude Questions and Answers
Question : 1
If x : y = 3 : 4 and y : z = 3 : 4, then ${x + y + z}/{3z}$ is equal to
a) $73/84$
b) $37/48$
c) $1/2$
d) $13/27$
Answer »Answer: (b)
x : y = 3 : 4 = 9 : 12
y : z = 3 : 4 = 12 : 16
x : y : z = 9 : 12 : 16
${x + y + z}/{3z} - {9k +12k +16k}/{3 × 16k} = 37/48$
Question : 2
If 177 is divided into 3 parts in the ratio $1/2 : 2/3 : 4/5$, then the second part is
a) 72
b) 60
c) 45
d) 75
Answer »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
Question : 3
To get the ratio p : q (for p ≠ q), one has to add a number to each term of the ratio x : y, the number is
a) ${px - qy}/{p - q}$
b) ${py - qx}/{p - q}$
c) ${qx - py}/{p - q}$
d) ${px + qy}/{p - q}$
Answer »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 =${qx - py}/{p - q}$
Question : 4
If $x/y = 3/4$, the ratio of (2x + 3y) and (3y - 2x) is
a) 1 : 1
b) 3 : 1
c) 3 : 2
d) 2 : 1
Answer »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
Question : 5
A and B together have Rs. 6300. If $5/19$ th of A’s amount is equal to $2/5$ th of B’s amount. The amount of ‘B’ is
a) Rs.2300
b) Rs.4000
c) Rs.3800
d) Rs.2500
Answer »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
Question : 6
If x : y = 3 : 4, then the value of (4x - y) : (2x + 3y) is
a) 4 : 3
b) 8 : 3
c) 8 : 9
d) 4 : 9
Answer »Answer: (d)
$x/y = 3/4$
${4x - y}/{2x +3y} ={4x/y-1}/{2x/y+3}$
= ${4 × 3/4 - 1}/{2× 3/4+ 3}$
= $2/{3/2+ 3} = {2× 2}/9 = 4 : 9$
GET ratio & proportion PRACTICE TEST EXERCISES
type 1 basic concepts of ratio & proportion
type 2 age based ratio & proportion problems
type 3 addition subtraction product on ratio & proportion
type 4 income & expenditure based ratio & proportion problems
type 5 shares & partnership based ratio & proportion problems
type 6 fractions based ratio & proportion problems
type 7 finding sum difference product based ratio & proportion problems
type 8 alligation & mixtures based ratio & proportion problems
type 9 coins & rupees based ratio & proportion problems
ratio & proportion Shortcuts and Techniques with Examples
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