model 11 percentage with ratios Section-Wise Topic Notes With Detailed Explanation And Example Questions

MOST IMPORTANT quantitative aptitude - 11 EXERCISES

Top 10,000+ Aptitude Memory Based Exercises

The following question based on percentage topic of quantitative aptitude

Questions : The difference of two numbers is 45% of their sum. The ratio of the larger number to the smaller number is

(a) 29 : 11

(b) 11 : 29

(c) 9 : 20

(d) 20 : 9

The correct answers to the above question in:

Answer: (a)

Let the numbers be x and y and x is greater than y.

Then x – y = 45% of (x + y)

x – y = $45/100(x + y)$

x – y = $9/20(x + y)$

20x – 20y = 9x + 9y

20x – 9x = 20y + 9y

11x = 29y

$x/y = 29/11$ or 29 : 11

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Read more ratios based Based Quantitative Aptitude Questions and Answers

Question : 1

The price of sugar is increased by 20%. If the expenditure on sugar has to be kept the same as earlier, the ratio between the reduction in consumption and the original consumption is

a) 1 : 6

b) 1 : 5

c) 1 : 4

d) 1 : 3

Answer: (a)

The raised price = $120/100$ of the former price

The householder must now consume $100/120$ of the original amount

The reduction in consumption = $(1 – 100/120)$ of the original consumption = $1/6$ of the original consumption

i.e. 1 : 6

Using Rule 8,

If the income of a man is A% more than another man, then income of another man is less in comparison to the 1st man by

$(A/(100 + A)× 100)%$

Required percentage = $(20/{100 + 20})×100$

= $20/120×100$ = $100/6$%

Required ratio = 1 : 6

Question : 2

The ratio of the number of boys to that of girls in a village is 3 : 2. If 30% of boys and 70% of girls appeared in an examination, the ratio of the number of villagers, appreared in the examination to that not appeared in the same examination is

a) 1 : 1

b) 27 : 23

c) 23 : 27

d) 9 : 14

Answer: (c)

Boys in the village = 3x

Girls in the village = 2x

Villagers who appeared in the examination

= ${3x × 30}/100 + {2x × 70}/100$

= ${9x}/10 + {14x}/10 = {23x}/10$

Villagers who did not appear in the examination

= ${3x × 70}/100 + {2x × 30}/100$

= ${21x}/10 + {6x}/10 = {27x}/10$

Required ratio = ${23x}/10 : {27x}/10$ = 23 : 27

Question : 3

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) 180

b) 200

c) 160

d) 100

Answer: (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

Question : 4

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) 70

b) 80

c) 78

d) 56

Answer: (c)

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%

Question : 5

The bus fare and train fare of a place from Kolkata were Rs.20 and Rs.30 respectively. Train fare has been increased by 20% and the bus fare has been increased by 10%. The ratio of new train fare to new bus fare is

a) 5 : 3

b) 3 : 5

c) 18 : 11

d) 11 : 18

Answer: (c)

Increased train fare = Rs.$(120/100 × 30)$= Rs.36

Increased bus fare = Rs.$(110/100 × 20)$ = Rs.22

Required ratio = 36 : 22 = 18 : 11

Question : 6

Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is

a) 4 : 5

b) 6 : 7

c) 3 : 5

d) 2 : 5

Answer: (a)

Let the third number be 100.

First number = 120; Second number = 150

Required ratio = $120/150$

= $4/5$ or 4 : 5

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