Problem 1.  In a restaurant’s kitchen, the ratio of chefs to kitchen helpers is 5:3. If there are 40 people working in the kitchen, how many chefs and kitchen helpers are there?

A. 25 chefs and 15 kitchen helpers
B. 20 chefs and 20 kitchen helpers
C. 30 chefs and 10 kitchen helpers
D. 15 chefs and 25 kitchen helpers

Correct Answer: A. 25 chefs and 15 kitchen helpers

Solution:
The total ratio of chefs to kitchen helpers given is 5:3, which sums up to 8 parts.

Calculate the Value of One Part:

To find out how many people make up one part of the ratio, divide the total number of people by the total number of parts.
Total people = 40, Total parts = 5 (chefs) + 3 (kitchen helpers) = 8 parts.
One part = 40/8 = 5

Calculate the Number of Chefs:

The number of chefs is 5 parts.
Number of chefs = 5 parts × 5 people per part = 25.

Calculate the Number of Kitchen Helpers:

The number of kitchen helpers is 3 parts.
Number of kitchen helpers = 3 parts × 5 people per part = 15.

Problem 2. In a school, the ratio of teachers to students is 1:20. If there are 105 teachers and students combined, how many teachers and students are there?

A. 5 teachers and 100 students
B. 10 teachers and 95 students
C. 15 teachers and 90 students
D. 20 teachers and 85 students

Answer: C. 15 teachers and 90 students

Solution:

Total ratio parts = 1 (teachers) + 20 (students) = 21 parts
Each part = 105 / 21 = 5
Teachers = 1 part × 5 = 5 teachers
Students = 20 parts × 5 = 100 students

Problem 3.  The ratio of cats to dogs in a pet shop is 4:3. If there are a total of 28 cats and dogs, how many cats and dogs are there?

A. 16 cats and 12 dogs
B. 12 cats and 16 dogs
C. 14 cats and 14 dogs
D. 20 cats and 8 dogs

Answer: A. 16 cats and 12 dogs

Solution:

Total ratio parts = 4 (cats) + 3 (dogs) = 7 parts
Each part = 28 / 7 = 4
Cats = 4 parts × 4 = 16 cats
Dogs = 3 parts × 4 = 12 dogs

Problem 4.  In a mixture of juice, the ratio of water to concentrate is 7:2. If the total volume of the mixture is 81 liters, how many liters of water and concentrate are there?

A. 63 liters of water and 18 liters of concentrate
B. 54 liters of water and 27 liters of concentrate
C. 49 liters of water and 32 liters of concentrate
D. 45 liters of water and 36 liters of concentrate

Answer: A. 63 liters of water and 18 liters of concentrate

Solution:

Total ratio parts = 7 (water) + 2 (concentrate) = 9 parts
Each part = 81 / 9 = 9
Water = 7 parts × 9 = 63 liters
Concentrate = 2 parts × 9 = 18 liters

Problem 5. The ratio of boys to girls in a club is 3:5. If there are 40 members in the club, how many boys and girls are there?

A. 15 boys and 25 girls
B. 18 boys and 22 girls
C. 12 boys and 28 girls
D. 20 boys and 20 girls

Answer: A. 15 boys and 25 girls

Solution:

Total ratio parts = 3 (boys) + 5 (girls) = 8 parts
Each part = 40 / 8 = 5
Boys = 3 parts × 5 = 15 boys
Girls = 5 parts × 5 = 25 girls

Problem 6. In a company, the ratio of managers to employees is 2:9. If the total number of managers and employees is 66, how many managers and employees are there?

A. 12 managers and 54 employees
B. 18 managers and 48 employees
C. 14 managers and 52 employees
D. 10 managers and 56 employees

Answer: A. 12 managers and 54 employees

Solution:

Total ratio parts = 2 (managers) + 9 (employees) = 11 parts
Each part = 66 / 11 = 6
Managers = 2 parts × 6 = 12 managers
Employees = 9 parts × 6 = 54 employees

Problem 7. The ratio of blue to red marbles in a bag is 3:7. If there are 50 marbles in total, how many blue and red marbles are there?

A. 15 blue and 35 red
B. 20 blue and 30 red
C. 25 blue and 25 red
D. 30 blue and 20 red

Answer: A. 15 blue and 35 red

Solution:

Total ratio parts = 3 (blue) + 7 (red) = 10 parts
Each part = 50 / 10 = 5
Blue = 3 parts × 5 = 15 blue
Red = 7 parts × 5 = 35 red

Problem 8.  The ratio of apples to oranges in a basket is 4:3. If there are 28 fruits in total, how many apples and oranges are there?

A. 16 apples and 12 oranges
B. 14 apples and 14 oranges
C. 12 apples and 16 oranges
D. 18 apples and 10 oranges

Answer: A. 16 apples and 12 oranges

Solution:

Total ratio parts = 4 (apples) + 3 (oranges) = 7 parts
Each part = 28 / 7 = 4
Apples = 4 parts × 4 = 16 apples
Oranges = 3 parts × 4 = 12 oranges

Problem 9. The ratio of adults to children at a movie theater is 5:2. If there are 42 people in total, how many adults and children are there?

A. 30 adults and 12 children
B. 25 adults and 17 children
C. 20 adults and 22 children
D. 35 adults and 7 children

Answer: A. 30 adults and 12 children

Solution:

Total ratio parts = 5 (adults) + 2 (children) = 7 parts
Each part = 42 / 7 = 6
Adults = 5 parts × 6 = 30 adults
Children = 2 parts × 6 = 12 children

Problem 10.  The ratio of fiction to non-fiction books in a library is 7:5. If there are 144 books in total, how many fiction and non-fiction books are there?

A. 84 fiction and 60 non-fiction
B. 70 fiction and 74 non-fiction
C. 80 fiction and 64 non-fiction
D. 90 fiction and 54 non-fiction

Answer: A. 84 fiction and 60 non-fiction

Solution:

Total ratio parts = 7 (fiction) + 5 (non-fiction) = 12 parts
Each part = 144 / 12 = 12
Fiction = 7 parts × 12 = 84 fiction
Non-fiction = 5 parts × 12 = 60 non-fiction

Problem 11.  The ratio of men to women in a committee is 3:4. If there are 56 members in the committee, how many men and women are there?

A. 21 men and 35 women
B. 24 men and 32 women
C. 28 men and 28 women
D. 18 men and 38 women

Answer: B. 24 men and 32 women

Solution:

Total ratio parts = 3 (men) + 4 (women) = 7 parts
Each part = 56 / 7 = 8
Men = 3 parts × 8 = 24 men
Women = 4 parts × 8 = 32 women

Problem 11

A total bonus of P360,000 is to be distributed among Juan, Maria, and Lena such that Juan receives three times as much as Maria, and Maria receives half as much as Lena. How much would Lena receive?

• A. P60,000
• B. P120,000
• C. P160,000
• D. P240,000

Answer: D. P240,000

Solution: Let Maria’s share be $m$.

Then, Juan’s share is $3m$, and Lena’s share is $2m$. The total bonus is given by: 3𝑚 + 𝑚 + 2𝑚 = 6𝑚 = 𝑃360,000.  𝑚 = 𝑃60,000 Thus, Lena’s share is: $2m=2\times P60,000=P120,000$ So, Lena receives P120,000.