# Ratios and Proportions Practice Quiz 3

5 Steps - 3 Clicks

# Ratios and Proportions Practice Quiz 3

### Introduction

Ratios and Proportions hold a significant place in several competitive exams including recruitment exams and college entrance exams. Ratios are a means to compare quantities and Proportions are a means to understand if ratios are equivalent. Ratios and Proportions Practice Quiz 3 will provide examples and solved questions to understand the significance of the topic. The Ratios and Proportions topic is crucial for all competitive exams including the Quantitative Aptitude section.

What are Ratios?[a:b or a to b or a/b]

Ratios are the mathematical numbers used to compare two entities which are similar to each other in terms of units. For example, we can compare the height of student 1 to the height of student 2. FACT: Properties/Elements that are not similar cannot be compared. Comparison of non-similar properties does not reveal any details of the entities being compared. Example: We can’t compare the height of a person to the weight of another person to determine who is taller. The ratio of a to b is represented as: a to b or a:b or a/b.

Ratios compare things similar to each other. The ratios are compared with each other using proportions. Proportion is an equation to represent that two ratios are equivalent. When two ratios are the same, they are said to be proportionate to each other or they are said to be in proportion. Proportions are represented by ‘::’ or ‘=’ sign. Proportions are primarily used to find missing quantities by using the fact that one ratio is equal to the other.

In simple terms, a ratio is a way to compare two quantities by using division. A proportion, on the other hand, is an equation that says that two ratios are equivalent. If one number in a proportion is unknown you can find that number by solving the proportion.

### Quiz

Q1. Chintu, Pintu and Mintu are three friends. Chintu is twice as old as Pintu and Mintu is as old as Cintu and Pintu together. Two years later, the ratio of age of Chintu and Mintu would be 7:10 what was the age of Pintu five years ago?

A. 2 years
B. 4 years
C. 5 years
D. 1 years
E. 8 years

Explanation – Let Pintu’s present age = x, Chintu = 2x and Mintu = x + 2x = 3x

Two years later $$[\frac{2x+2}{3x+2}]$$ = $$(\frac{7}{10})$$

20x + 20 = 21x + 14

x = 6

Pintu’s present age = 6

Five years ago, his age was 6 – 5 = 1 year

Q2. In a school, students of class I and class II are going for a picnic to Surajkund and Badkal lake respectively. The ratio f number of students in class I and II is 5:3. Also the ratio of the contribution made by each student of class I and II is 19:17. If the total contribution made by the all the students of both the class is Rs.29200, then find the total contribution made by class II students only

A. Rs.10950
B. Rs.13789
C. Rs.10200
D. Rs.13272
E. None of these

Explanation – Let the no. of students in class II be 5x and 3x respectively and contribution made by each student of class I and class II be 19y and 17y respectively.

Hence, ratio of total contribution of class I and class II = 5x × 19y : 3x × 17y = 95 : 51

Total contribution made by students of class II ($$\frac{51}{(95+51)}$$) × 29200 = 10200

Q3. A donkey moves at a speed of 8 kmph, when no load is put on him. Reduction in the speed of donkey varies directly to the square root of the kgs of load put on him. When only 4 kgs of load is put the speed of the donkey becomes 6 kmph. Find the minimum load that can be put on the donkey with which it cannot move.

A. 64 kg
B. 63.9 kg
C. 65.2 kg

D. Cannot be determined
E. None of these

Explanation – Speed of the donkey, Without any load = 8 kmph. With 4 kgs of load, speed becomes 6 kmph, hence speed is reduced by 2 kmph.

Reduction in speed varies directly with the square root of the load.

Hence (8 – 6) = k√4 = k ± 1

The donkey cannot move at zero speed. i.e. when his speed reduced by 8 kmph. So reduction in speed = 8 kmph

8 = 1√l => √l = 8 and l = 64, when √l = -8, l = 64

At 64 kg the donkey will stop.

Q4. A container has a mixture of kerosene and castor oil in the ratio of 7:5 and another container contains kerosene and castor oil in the ratio of 5:3. Find the proportion in which the mixtures from two containers should be mixed so that the resultant mixture has ratio of kerosene and castor oil of 3:2.

A. 2:3
B. 3:2
C. 4:1
D. 5:2
E. None of these

Explanation – Let quantity of mixture taken from first be x and second be y.

Amount of kerosene oil in the resultant mixture (x + y) is

($$\frac{7}{12}$$)x + ($$\frac{5}{8}$$)y = ($$\frac{3}{5}$$)(x + y)

($$\frac{7}{12}$$)x – ($$\frac{3}{5}$$)x = ($$\frac{3}{5}$$)y – ($$\frac{5}{8}$$)y – ($$\frac{1}{60}$$)x = -($$\frac{1}{40}$$)y => ($$\frac{x}{y}$$) = ($$\frac{6}{4}$$) = ($$\frac{3}{2}$$) = 3 : 2

Q5. There are three vessels 1, 2 and 3. The ratio of the total capacity of vessels 1, 2 and 3 is 5:4:3 respectively. All the vessels are full of mixture of sugar syrup and water. In vessel 1, ratio of sugar syrup to water is 2:3. Similar ratio in case of vessel 2 and vessel 3 is 5:4 and 1:3 respectively. The mixture of all the three vessels is emptied into one bigger vessel. What is the resulting ratio of sugar syrup and water?

A. 17:25
B. 179:253
C. 253:179
D. 233:169
E. None of these

Explanation – Let the total mixture in vessel 1,2 and 3 be 5 litres and 3 litres respectively. So, quantity of water in (5 + 4 + 3) = 12 litres of mixture is

= ($$\frac{3}{5}$$)×5 + ($$\frac{4}{9}$$)×4 + ($$\frac{3}{4}$$)×3

= 3 + ($$\frac{16}{9}$$) + ($$\frac{9}{4}$$) = ($$\frac{108+64+81}{36}$$) = ($$\frac{253}{36}$$)

Quantity of sugar syrup is

12 – ($$\frac{253}{36}$$) = ($$\frac{179}{36}$$)

Ratio of sugar syrup to water = 179 : 253

Q1. A particular sum was divided among A, B and C in ratio 2:6:7 respectively. If the amount received by A was Rs. 4,908, what was the difference between the amounts received by B and C?

A. Rs. 2,454
B. Rs. 3,494
C. Rs. 2,135
D. Rs. 2,481
E. None of these

Explanation – If the total amount be Rs. x, then ($$\frac{2x}{15}$$) = 4908

x = $$\frac{(4908 × 15)}{2}$$ = Rs. 36810

Required difference = ($$\frac{(7 – 6)}{15}$$) × 36810 = Rs. 2454

Q2. The average age of a man and his son is 30 years. The ratio of their ages four years ago was 10:3 respectively. What is the difference between the present ages of the man and his son?

A. 28 years
B. 16 years
C. 26 years
D. 44 years
E. None of these

Explanation – Four years ago,

Father’s age = 10x years , son’s age = 3x years

10x + 3x + 8 = 60 (sum of their ages = 2 × 30 = 60)

= 13x = 60 – 8

= x = 4

Required difference

Q3. The ratio between Gloria’s and Sara’s present ages is 4:7 respectively, Two years ago the ratio between their ages was 1:2 respectively. What will be Sara’s age three years hence?

A. 17 years
B. 14 years
C. 11 years
D. 8 years
E. None of these

Explanation – Let Gloria’s and Sara’s present ages be 4x and 7x years respectively

Two years ago, $$\frac{(4x – 2)}{(7x – 2)}$$ = $$\frac{1}{2}$$

8x – 4 = 7x – 2

x = 2

Sara’s age three years hence = 7x + 3 = 17 years

Q4. The total number of students in a school is 31700. If the ratio of boys to the girls in the school is 743:842 respectively, what is the total number of girls
in the school?

A. 14860
B. 16480
C. 15340
D. Cannot be determined
E. None of these

Explanation – .Boys : Girls = 743 : 842

Total number of students = 31700

Number of girls = ($$\frac{842}{(743 +842)}$$) × 31700 = ($$\frac{842}{1585}$$) × 31700

= 16840

Q5. A sum of Rs. 10,980 is to be divided amongst A, B and C in the ratio 7:3:5 respectively. How much is C’s share?

A. Rs. 3,600
B. Rs. 3,006
C. Rs. 3,650
D. Rs. 3,660
E. Rs. 3,124

Explanation – C’s share = ($$\frac{5}{15}$$) × 10980 = Rs. 3660

Q1. In a class of 60 students, where the girls are twice that of boys. Kamal ranked seventeenth from the top. If there are 9 girls ahead of Kamal, the number of boys in rank after him is:

A. 3
B. 7
C. 12
D. 13
E. None of these

Explanation – Girls : Boys = 2 : 1. Total no.of students is 60

Girls 60 × ($$\frac{2}{3}$$) = 40 and boys = 20. Kamal has been ranked 17 which means there are 16 students before him of which 9 are girls remaining 7 are boys.

7 boys are ahead of Kamal + Kamal is the 8$$^{th}$$ boy, hence, there are (20 – 8) = 12 boys after him.

Q2. Two varieties of rice at Rs. 10 per kg and Rs. 12 per kg are mixed together in the ratio 1 : 2. What is the price of the resulting mixture?

A. Rs. 10.50 per kg
B. Rs. 10.67 per kg
C. Rs. 11.20 per kg
D. Rs. 11.33 per kg
E. None of these

Explanation – Let the amount of rice be 1 kg and 2 kg. (The given ratio is 1 : 2). So, total cost = 10 × 1 + 12 × 2 = 10 + 24 = 34

Rs. 34 is the cost of (1 + 2 = 3) kg of rice.

Cost per kg = ($$\frac{34}{3}$$) = 11.33 per kg

Q3. 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 did not get scholarship is:

A. 68%
B. 78%
C. 82%
D. 72%
E. None of these

Explanation – Number of students in school = 100 (let)

Boys = ($$\frac{3}{5}$$) × 100 = 60, Girls = 40

Students who did not get scholarship

Boys = 60 × ($$\frac{80}{100}$$) = 48

Girls = 40 × ($$\frac{75}{100}$$) = 30

Students who do not get scholarship = 78

Required percentage = 78

Q4. In a mixture of 60 litres, the ratio of acid and water is 2 : 1. If the ratio of acid and water is to be 1 : 2, then the amount of water (in litres) to be added to the mixture is

A. 50
B. 45
C. 55
D. 60
E. None of these

Explanation – In 60 litres of mixture,

Acid = ($$\frac{2}{3}$$) × 60 = 40 litres, Water = 20 litres

If x litres of water be mixed, then ($$\frac{40}{(20 + x)}$$)= 80

x = 80 – 20 = 60 litres

Q5. Salaries of Akash, Babloo and Chintu are in the ratio of 2 : 3 : 5. If their salaries were increased by 15%, 10% and 20% respectively, what will be the new ratio of their salaries?

A. 3 : 3 : 10
B. 23 : 33 : 60
C. 20 : 22 : 40
D. Cannot be determined
E. None of these

Explanation – .Required ratio = ($$\frac{(2 × 115)}{100}$$) : ($$\frac{(3 × 110)}{100}$$) : ($$\frac{(5 × 120)}{100}$$) 230 : 330 : 600 = 23 : 33 : 60

### Exams

Competitive Exams – College Entrance Exams
Diploma NITC New Delhi Goa Diploma Admissions 2019
PG GATE ATMA 2019

Competitive Exams – Recent Job Notifications
Category
Banking SSC Railway
Defence Police Insurance