The problem can be solved by working backward from the given information. We are given the number of very tall boys and their proportion among all boys. From this, we can find the total number of boys. Then, using the proportion of boys to the total number of students, we can find the total number of students. Finally, by subtracting the number of boys from the total number of students, we can determine the number of girls.
Correct Option: B) 12
Consider the following statements:
1. Either A and B are of the same age or A is older than B
2. Either C and D are of the same age or D is older than C
3. B is older than C
Which of the following conclusions can be drawn from the above statements?
A is older than B
B and D are of the same age
D is older than C
A is older than C
This problem involves logical deduction based on given statements about the ages of four individuals (A, B, C, D). We need to analyze each statement and combine them to find a conclusive relationship between the ages.
Correct Option: D) A is older than C
This problem can be solved using the concept of weighted average or by setting up equations based on the definition of average. We are given the overall average salary and the average salaries for male and female employees. We need to find the percentage of male employees. We can assume the total number of employees or use a ratio approach.
Let \(M\) be the number of male employees and \(F\) be the number of female employees.
The total number of employees is \(T = M + F\).
The average salary for all employees is given as Rs. 5000.
So, the total salary paid to all employees is \(5000 \times (M + F)\).
The average salary for male employees is Rs. 5200.
So, the total salary paid to male employees is \(5200 \times M\).
The average salary for female employees is Rs. 4200.
So, the total salary paid to female employees is \(4200 \times F\).
The sum of total salaries paid to male and female employees must equal the total salary paid to all employees:
\[ 5200M + 4200F = 5000(M + F) \]Now, let's simplify the equation:
\[ 5200M + 4200F = 5000M + 5000F \]Rearrange the terms to group \(M\) and \(F\):
\[ 5200M - 5000M = 5000F - 4200F \]\[ 200M = 800F \]Find the ratio of \(M\) to \(F\):
\[ \frac{M}{F} = \frac{800}{200} \]\[ \frac{M}{F} = \frac{4}{1} \]This means for every 4 male employees, there is 1 female employee. So, if \(M=4k\) and \(F=1k\), then the total number of employees is \(T = 4k + 1k = 5k\).
We need to find the percentage of male employees:
\[ \text{Percentage of males} = \frac{\text{Number of males}}{\text{Total number of employees}} \times 100\% \]\[ \text{Percentage of males} = \frac{M}{M + F} \times 100\% \]\[ \text{Percentage of males} = \frac{4k}{4k + 1k} \times 100\% \]\[ \text{Percentage of males} = \frac{4k}{5k} \times 100\% \]\[ \text{Percentage of males} = \frac{4}{5} \times 100\% \]\[ \text{Percentage of males} = 0.8 \times 100\% \]\[ \text{Percentage of males} = 80\% \]B) The percentage of males employed in the company is 80%.
Directions for the following 3 (three) items:
Consider the following information and answer the three items that follow:
Six boxes A, B, C, D, E and F have been painted with six different colours viz., violet, indigo, blue, green, yellow and orange and arranged from left to right(not necessarily either kept or painted with the colours in the same order). Each box contains a ball of any one of the following six games: cricket, hockey, tennis, golf, football and volleyball (not necessarily in the same order). The golf ball is in violet box and is not in the box D. The box A which contains tennis ball is orange in colour and is at the extreme right. The hockey ball is neither in box D nor in box E. The box C having cricket ball is painted green. The hockey ball is neither in the box painted blue nor in the box painted yellow. The box C is fifth from right and next to box B. The box B contains volleyball. The box containing the hockey ball is between the boxes containing golf ball and volleyball.
Which one of the following boxes contains the golf ball?
The question asks to identify the color of the box containing the football. This is a logical reasoning question based on visual information. We need to carefully observe the provided image and determine if there is enough information to answer the question definitively.
Upon careful observation of the image, the football is shown inside a box. However, the color of this specific box is not clearly discernible. It appears to be partially obscured or drawn in a way that its color cannot be definitively identified as yellow, indigo, or blue. The image does not provide sufficient information to assign a specific color to the box holding the football.
C) Cannot be determined as data are inadequate. The image does not clearly show the color of the box containing the football, making it impossible to determine its color with certainty.
To find the percentage by which Y is less than X, we first need to express X and Y in terms of Z. We can assume a value for Z (e.g., 100) to simplify calculations, or use a variable. Then, we calculate the difference between X and Y and express it as a percentage of X.
Correct Option: B) 10%
To construct a closed cube from a rectangular piece of tin, the area of the tin must be equal to the total surface area of the cube. We will first calculate the area of the rectangular tin and then use the formula for the total surface area of a cube to find the side length of the cube.
Calculate the area of the rectangular tin:
The length of the rectangle is \(L = 12 \text{ cm}\).
The width of the rectangle is \(W = 8 \text{ cm}\).
The area of the rectangle is given by:
Relate the area of the tin to the surface area of the cube:
When the tin is used to construct a closed cube, the area of the tin is equal to the total surface area of the cube.
Use the formula for the total surface area of a cube:
Let the side of the cube be \(a\). A cube has 6 identical square faces. So, the total surface area of a cube is given by:
Solve for the side of the cube (\(a\)):
Equating the two expressions for the total surface area:
C) 4 cm — The side of the cube is 4 cm, as calculated by equating the area of the tin to the total surface area of the cube.
The problem asks for the maximum number of candidates such that no two candidates have an identical sequence of answers to five questions, where each question has two choices (True or False). This is a problem of counting the total number of possible unique answer sequences.
Identify the number of questions: There are 5 questions.
Identify the number of choices per question: Each question has 2 choices: True (T) or False (F).
Calculate the number of possible answer sequences for one question: For the first question, there are 2 choices (T or F).
Calculate the number of possible answer sequences for five questions: Since the choice for each question is independent, we multiply the number of choices for each question to find the total number of unique sequences.
Total number of unique answer sequences \( = 2 \times 2 \times 2 \times 2 \times 2 \).
Compute the total number:
\[ 2^5 = 32 \]
Relate to the number of candidates: It is given that no two candidates have given identical answers. This means each candidate must have a unique answer sequence. Therefore, the maximum number of candidates is equal to the total number of unique answer sequences possible.
Maximum number of candidates \( = 32 \).
D) 32 — The total number of unique answer combinations for 5 questions, each with 2 choices, is \(2^5 = 32\). Since no two candidates can have identical answer sequences, the maximum number of candidates is 32.