# Ratio and Proportion

### If the numerator and denominator of a proper fraction are increased

If the numerator and denominator of a proper fraction are increased by the same positive quantity which is greater than zero, the resulting fraction is

1. always less than the original fraction
2. always greater than the original fraction
3. always equal to the original fraction
4. such that nothing can .be claimed definitely

### X, Y and Z are three contestants in a race of 1000 m

X, Y and Z are three contestants in a race of 1000 m. Assume that all run with different uniform speeds. X gives Y a start of 40 m and X gives Z a start of 64 m. If Y and Z were to compete in a race of 1000 m, how many metres start will Y give to Z?

1. 20
2. 25
3. 30
4. 35

### The ratio of a two-digit natural number to a number formed by reversing its digits is 4:7

The ratio of a two-digit natural number to a number formed by reversing its digits is 4:7. The number of such pairs is

1. 5
2. 4
3. 3
4. 2

### The cost of a diamond varies directly as the square of its weight

The cost of a diamond varies directly as the square of its weight. A diamond broke into four pieces with their weights in the ratio of 1:2:3:4. If the loss in total value of the diamond was the ₹ 70,000, what was the price of the original diamond?

1. ₹ 1,00,000
2. ₹ 1,40,000
3. ₹ 1,50,000
4. ₹ 1,75,000

### In a class of 49 students, the ratio of girls to boys is 4:3

In a class of 49 students, the ratio of girls to boys is 4:3. If 4 girls leave the class, the ratio of girls to boys would be

1. 11:7
2. 8:7
3. 6:5
4. 9:8

### The ratio of two numbers is 1:5 and their product is 320

The ratio of two numbers is 1:5 and their product is 320. What is the difference between the squares of these two numbers?

1. 1024
2. 1256
3. 1536
4. 1640

### The angles of a triangle are in the ratio 2:4:3. The smallest angle of the triangle is

The angles of a triangle are in the ratio 2:4:3. The smallest angle of the triangle is

1. 20°
2. 40°
3. 50°
4. 60°

### The areas of two circular fields are in the ratio 16 : 49

The areas of two circular fields are in the ratio 16 : 49. If the radius of the bigger field is 14 m, then what is the radius of the smaller field?

1. 4 m
2. 8 m
3. 9 m
4. 10 m

### In a certain school, the ratio of boys and girls is 7 : 5

In a certain school, the ratio of boys and girls is 7 : 5. If there are 2400 students in the school, then how many girls are there?

1. 500
2. 700
3. 800
4. 1000

### Age of X is 6 times that of Y. After 4 years

Age of X is 6 times that of Y. After 4 years, X is 4 times elder to Y. What is the present age of Y?

1. 4 yr
2. 5 yr
3. 6 yr
4. 7 yr

### Two numbers are in the ratio 3:5. If 9 is subtracted from each number

Two numbers are in the ratio 3:5. If 9 is subtracted from each number, then they are in the ratio of 12:23. What is the second number?

1. 44
2. 55
3. 66
4. 77

### The costs of two articles are in the ratio 3:5

The costs of two articles are in the ratio 3:5. If there is 30% loss on the first article and 20% gain on the second article, what is the overall percentage of loss or gain?

1. 2% loss
2. 2.25% gain
3. 5.25% loss
4. 1.25% gain

### In a 500 metres race, B starts 45 metres ahead of A

In a 500 metres race, B starts 45 metres ahead of A, but A wins the race while B is still 35 metres behind. What is the ratio of the speeds of A to B assuming that both start at the same time?

1. 25:20
2. 25:21
3. 5:7
4. 5:3

### Two equal glasses of same type are respectively 1/3 and 1/4 full

Two equal glasses of same type are respectively 1/3 and 1/4 full of milk. They are then filled up with water and the contents are mixed in a pot. What is the ratio of milk and water in the pot?

1. 9 : 21
2. 11 : 23
3. 7 : 17
4. 1 : 3

### The monthly incomes of Peter and Paul are in the ratio of 4:3

The monthly incomes of Peter and Paul are in the ratio of 4:3. Their expenses are in the ratio of 3:2. If each saves Rs. 6,000 at the end of the month, their monthly incomes respectively are (in Rs.)

1. 24,000 and 18,000
2. 28,000 and 21,000
3. 32,000 and 24,000
4. 34,000 and 26,000

### In a rare coin collection, there is one gold coin

In a rare coin collection, there is one gold coin for every three non-gold coins. 10 more gold coins are added to the collection and the ratio of gold coins to non-gold coins would be 1:2. Based on the information; the total number of corns in the collection now becomes

1. 90
2. 80
3. 60
4. 50

### Two glasses of equal volume are respectively half and three-fourths filled

Two glasses of equal volume are respectively half and three-fourths filled with milk. They are then filled to the brim by adding water. Their contents are then poured into another vessel. What will be the ratio of milk to water in this vessel?

1. 5:3
2. 1:3
3. 3:2
4. 2:3

### The rabbit population in community A increases at 25% per year

The rabbit population in community A increases at 25% per year while that in community B increases at 50% per year. If the present populations of A and B are equal, what will he the ratio of the number of rabbits in community B to that in community A after 2 years?

1. 1.44
2. 1.72
3. 1.90
4. 1.26

### Two types of tea, A and B, are mixed and then sold at Rs. 40 per kg

Two types of tea, A and B, are mixed and then sold at Rs. 40 per kg. The profit is 10% if A and B are mixed in the ratio 3 : 2, and 5% if this ratio is 2 : 3. The cost prices, per kg, of A and B are in the ratio

1. 18 : 25
2. 19 : 24
3. 21 : 25
4. 17 : 25

### Raju and Lalitha originally had marbles in the ratio 4:9

Raju and Lalitha originally had marbles in the ratio 4:9. Then Lalitha gave some of her marbles to Raju. As a result, the ratio of the number of marbles with Raju to that with Lalitha became 5:6. What fraction of her original number of marbles was given by Lalitha to Raju?

1. 1/4
2. 7/33
3. 1/5
4. 6/19

### A fraction, which bears the same ratio to 1/27, that 3/11 does to 5/9

A fraction, which bears the same ratio to 1/27, that 3/11 does to 5/9, is equal to

1. 1/11
2. 3/11
3. 1/55
4. 55

### A, B and C enter into a partnership and their shares are in ratio 1/2 : 1/3 : 1/4

A, B and C enter into a partnership and their shares are in ratio 1/2 : 1/3 : 1/4, after 2 months, A withdraws half of his capital and after 10 months, a profit of Rs 378 is divided among them. What is B's share?

1. Rs 124
2. Rs 144
3. Rs 156
4. Rs 165

### From each of the two given numbers, half the smaller number is subtracted

From each of the two given numbers, half the smaller number is subtracted. Of the resulting numbers the larger one is three times as large as the smaller. What is the ratio of the two numbers?

1. 2 : 3
2. 3 : 2
3. 3 : 1
4. 2 : 1

### In a certain examination, the number of students who passed, was three times

In a certain examination, the number of students who passed, was three times the number of those who were rejected. If there had been 16 fewer candidates and if six more had been rejected, the number of those who passed and of those who were rejected would have been in the ratio 2 : 1. Find the number of candidates?

1. 120
2. 130
3. 136
4. 156

### The sum of three numbers is 98. If the ratio of the first to the second is 2:3

The sum of three numbers is 98. If the ratio of the first to the second is 2 : 3 and that of the second to the third is 5 : 8, then the second number is

1. 20
2. 30
3. 48
4. 58

### A milkman mixes 20 litres of water with 80 litres of milk. After selling one-fourth

A milkman mixes 20 litres of water with 80 litres of milk. After selling one-fourth of this mixture, he adds water to replenish the quantity that he had sold. What is the current proportion of water to milk?

1. 3 : 4
2. 2 : 3
3. 1 : 3
4. 1 : 2

### A milkman mixes 20 L of water with 80 L of milk. After selling one-fourth of this mixture

A milkman mixes 20 L of water with 80 L of milk. After selling one-fourth of this mixture, he adds water to replenish the quantity that he has sold. What is the current proportion of water to milk?

1. 2 : 3
2. 1 : 2
3. 1 : 3
4. 2 : 1

### If a, b, c are three positive integers such that a and b are in the ratio 3:4

If a, b, c are three positive integers such that a and b are in the ratio 3 : 4 while b and c are in the ratio 2 : 1, then which one of the following is a possible value of (a + b + c)?

1. 201
2. 205
3. 207
4. 210

### A can contains a mixture of two liquids A and B is the ratio 7:5

A can contains a mixture of two liquids A and B is the ratio 7:5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7:9. How many litres of liquid A was contained by the can initially?

1. 10
2. 20
3. 21
4. 25