Practice Fractions based ratio and proportion problems - quantitative aptitude Online Quiz (set-1) For All Competitive Exams
Q-1) Two numbers are in the ratio 1$1/2 : 2 2/3$, when each of these is increased by 15, they are in the ratio 1$2/3 : 2 1/2$ . The greater of the numbers
(a)
(b)
(c)
(d)
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
Q-2) If 177 is divided into 3 parts in the ratio $1/2 : 2/3 : 4/5$, then the second part is
(a)
(b)
(c)
(d)
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
Q-3) If x : y = 3 : 4, then the value of (4x - y) : (2x + 3y) is
(a)
(b)
(c)
(d)
$x/y = 3/4$
${4x - y}/{2x +3y} ={4x/y-1}/{2x/y+3}$
= ${4 × 3/4 - 1}/{2× 3/4+ 3}$
= $2/{3/2+ 3} = {2× 2}/9 = 4 : 9$
Q-4) If $x/y = 3/4$, the ratio of (2x + 3y) and (3y - 2x) is
(a)
(b)
(c)
(d)
$x/y = 3/4$ (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
Q-5) Find the fraction which bears the same ratio to $1/27$ that $3/7$ does to $5/9$.
(a)
(b)
(c)
(d)
Let the required fraction be x.
According to the question,
$x : 1/27 = 3/7 : 5/9$
$x × 5/9 = 1/27 × 3/7 = 1/63$
$x = 1/63 × 9/5 = 1/35$
Q-6) Rs. 782 is divided into three parts in the ratio $1/2 : 2/3 : 3/4$, the first part is
(a)
(b)
(c)
(d)
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
Q-7) 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)
(b)
(c)
(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
Q-8) If x : y = 3 : 4 and y : z = 3 : 4, then ${x + y + z}/{3z}$ is equal to
(a)
(b)
(c)
(d)
x : y = 3 : 4 = 9 : 12
y : z = 3 : 4 = 12 : 16
x : y : z = 9 : 12 : 16
${x + y + z}/{3z} - {9k +12k +16k}/{3 × 16k} = 37/48$
Q-9) If A : B = $1/2 : 1/3$, B : C = $1/5 : 1/3$, then (A + B) : (B + C) is equal to
(a)
(b)
(c)
(d)
A : B = $1/2 : 1/3$ = 3 : 2
B : C = $1/5 : 1/3$ = 3 : 5
$A/B = 3/2$
${A+B}/B = {3+2}/2 = 5/2$
$B/C = 3 : 5 ⇒ C/B = 5/3$
${C+B}/B = 5/3 + 1 = 8/3$
${A+B}/{C+B} = 5/2 ÷ {8/3}$
= $5/2 × 3/8 = 15/16$ = 15 : 16
Q-10) The reciprocals of the squares of the numbers 1$1/2$ and 1$1/3$. are in the ratio
(a)
(b)
(c)
(d)
Ratio of the squares of $3/2$ and $4/3$
= $9/4 : 16/9$
Ratio of their reciprocals = $4/9 : 9/16$ = 64 : 81