Practice Ratios based - quantitative aptitude Online Quiz (set-1) For All Competitive Exams
Q-1) The ratio of the number of boys and girls in a school is 2 : 3. If 25% of the boys and 30% of the girls are scholarship holders, the percentage of the school students who are not scholarship holders is
(a)
(b)
(c)
(d)
Boys in school = 2x
Girls = 3x
Students who are not scholarship holders :
Boys ⇒ ${2x × 75}/100 = {6x}/4$
Girls ⇒ ${3x × 70}/100 = {21x}/10$
Total students who donot hold scholarship = ${6x}/4 + {21x}/10$
= ${30x + 42x}/20 = {72x}/20 = {18x}/5$
Required percentage = ${{18x}/5}/{5x} ×100$ = 72%
Q-2) There is a ratio of 5: 4 between two numbers. If 40 % of the first number is 12, then what would be 50 % of the second number?
(a)
(b)
(c)
(d)
Let the numbers be 5x and 4x respectively
According to the question,
5x × $40/100$ = 12
2x = 12 ⇒ x = 6
4x of 50% = 4 × 6 × $1/2$ = 12
Q-3) The ratio of the number of boys and girls in a school is 3:2. If 20% of the boys and 25% of the girls are scholarship holders, the percentage of the school students who are not scholarship holders is
(a)
(b)
(c)
(d)
Let the number of students in school be 100.
Boys ⇒ 60 Girls ⇒ 40
Students who do not hold scholarship :
Boys ⇒ ${60 × 80}/100$ = 48 Girls ⇒ ${40 × 75}/100$ = 30
Required answer = 48 + 30 = 78 i.e., 78%
Q-4) Rama's expenditures and savings are in the ratio 5 : 3. If her income increases by 12% and expenditure by 15%, then by how much per cent do her savings increase ?
(a)
(b)
(c)
(d)
Let Rama's expenditure = 5x
Savings = 3x
Rama's income = 5x + 3x = 8x
After increase,
Rama's income = $112/100 × 8x = 8.96 x$
Rama's expenditure = ${5x × 115}/100 = 5.75x$
Rama's savings = (8.96x – 5.75x) = 3.21x
Rama's saving percent = $({3.21x - 3x}/{3x})×100$
= $0.21/3 × 100 = 7$
Q-5) The ratio of the number of boys and girls in a college is 3 : 2. If 20% of boys and 25% of girls are adults, the percentage of those students who are not adults, is
(a)
(b)
(c)
(d)
Let the number of boys and girls in the college be 3x and 2x respectively.
Number of minor boys = $3x × 80/100 = {12x}/5$
Number of minor girls = $2x × 75/100 = {3x}/2$
Total number of minor students = ${12x}/5 + {3x}/2$
= ${24x + 15x}/10 = {39x}/10 $
Required percentage = ${39x}/{10 × 5x} × 100$ = 78%
(As total students = 3x + 2x)
Q-6) The ratio of the number of boys to that of girls in a school is 4 : 1. If 75% of boys and 70% of the girls are scholarship-holders, then the percentage of students who do not get scholarship is
(a)
(b)
(c)
(d)
Let the number of boys and girls be 4x and x respectively.
Number of boys who hold scholarship. = $75/100 × 4x = 3x$
and number of girls who hold scholarship = ${70 × x}/100 = {7x}/10$
Number of students who do not hold scholarship
= $5x - 3x - {7x}/10 = 2x - {7x}/10$
= ${20x - 7x}/10 = {13x}/10$
The required percentage = ${{13x}/10}/{5x} × 100$
= ${13x}/{10 × 5x} × 100 = 26$%
Q-7) The ratio of the number of boys and girls in a school is 3 : 2. If 20% of the boys and 30% of the girls are scholarship holders, then the percentage of students, who do not get scholarship, is
(a)
(b)
(c)
(d)
Let the number of boys = 3x and that of girls = 2x
Number of boys who do not hold scholarship = 80% of 3x
= $3x × 80/100 = {12x}/5$
Number of girls who do not hold scholarship
= $2x × 70/100 = {14x}/10$
Number of students who do not hold scholarship
= ${12x}/5 + {14x}/10 = {24x + 14x}/10 = {38x}/10$
Required percentage = ${{38x}/10}/{5x} × 100 = 38/{10 × 5} × 100=76%$
Q-8) The ratio 5 : 4 expressed as a per cent equals :
(a)
(b)
(c)
(d)
5 : 4 when expressed as percent
= $5/4$ × 100 = 125%
Q-9) Two numbers are in the ratio 2 : 3. If 20% of the smaller number added to 20 is equal to the sum of 10% of the larger number and 25, then the smaller number is
(a)
(b)
(c)
(d)
Let the numbers be 2x and 3x.
According to the question,$(20/100 × 2x) + 20$
= $(10/100 × 3x) + 25$
${2x}/5 + 20 = {3x}/10 + 25$
${2x}/5 - {3x}/10$ = 25 - 20
${4x - 3x}/10$ = 5 ⇒ x = 50
The smaller number = 2x = 100
Q-10) The ratio of the number of boys and girls in a school is 3 : 2. If 20% of the boys and 25% of the girls are scholarship holders, then the percentage of the students, who do not get the scholarship, is :
(a)
(b)
(c)
(d)
Boys = 30, Girls = 20 (let)
Boys getting no scholarship = 24
Girls getting no scholarship = 15
Sum = 24 + 15 = 39
Required percentage = $39/50 × 100$ = 78%