In a certain room the ratio of males to females is 4 to 5. After 8 males enter the room, the ratio of males to females is 6 to 5. What is the total number of people in the room before the additional males enter the room?
Correct answer: B. 36
- A. 27
- B. 36
- C. 45
- D. 54
Explanation
To solve this problem, start by defining variables for the number of males and females in the room. Let the number of males be 4x and the number of females be 5x, based on the initial ratio of 4 to 5.The equation for the initial setup is: 4x / 5x = 4 / 5 (which holds true by definition)When 8 additional males enter, the number of males becomes 4x + 8. The new ratio of males to females is given as 6 to 5:(4x + 8) / 5x = 6 / 5Cross-multiply to solve for x: 5(4x + 8) = 6(5x) 20x + 40 = 30x 10x = 40 x = 4Substitute x back to find the number of males and females: Number of males = 4x = 16 Number of females = 5x = 20The total number of people initially in the room is 16 + 20 = 36. Thus, the correct answer is (B) 36.Options A, C, and D result from incorrect calculations or assumptions in setting up the problem or solving the equations.
Report an error
The more specific you are, the faster it gets fixed. A source beats an opinion.
Prefer email? [email protected]
About Quantitative Reasoning
Quantitative reasoning applies arithmetic and basic algebra to numerical relationships, including percentages, ratios, averages, fractions, proportions, profit and loss, rates, time, work and measurement. Questions focus on translating words into equations, choosing an efficient method and checking whether the result is numerically reasonable.
Practise Quantitative Reasoning
625 free Quantitative Reasoning MCQs from Analytical and Logical Reasoning, each with the correct answer and an explanation. Unlimited attempts, no account needed.
Discussion
Stuck on an option, or know a faster way to get there? Ask or explain it here.
No comments yet. Be the first to explain this one.
Exams that ask Analytical and Logical Reasoning questions like this
Analytical and Logical Reasoning is on 27 papers prepared for on TestUstad, and all of them draw the same bank, so this question is worth knowing for every one of them.
More Quantitative Reasoning questions
A tree is 8 feet tall and grows 8 inches each year. In how many years will the tree reach a height of 30 feet?
A 32-acre field yields 768 bushels of corn each year. How many more acres are needed to yield 960 bushels of corn each year?
If ¾ quart of lemonade concentrate is mixed with 6 ⅔ quarts of water to make lemonade for 40 people, how many quarts of lemonade concentrate are needed to make the lemonade for 24 people?
A person is born every 5 seconds and a person dies every 12 seconds. How many seconds does it take for the population to grow by one person?
Which of the following is equivalent to 0.03 % of 4?
The quantities x and y are positive. If x is decreased by 20 percent and y is increased by 20 percent, then the product of x and y is