To determine the percentage of time spent in school, we first need to know the proportion of the pie chart representing school hours. A circle has a total of 360 degrees. The pie chart gives us the number of degrees corresponding to school time.
Step 1: Identify the degrees of school time from the pie chart. Assume the pie chart shows school time as \( x \) degrees.
Step 2: Calculate the hours spent in school. Given \( 24 \) hours in a day:
To determine the percentage of time a student spends on games in comparison to sleeping, we need to calculate the hours spent on each activity using the given pie chart degrees and then compare them.
Step 1: Convert Degrees to Hours
Since a full circle is 360 degrees and a day has 24 hours, each degree represents: Hours per Degree = 24 / 360 = 1/15
Let the degrees allocated for games and sleeping be \(x\) and \(y\) respectively. These will be visible from the pie chart.
Step 2: Calculate Hours for Games and Sleeping
Hours for Games = \(x \times (1/15)\)
Hours for Sleeping = \(y \times (1/15)\)
Step 3: Calculate Percentage of Game Time Compared to Sleeping
The percentage comparison is given by: \((\text{Hours for Games} / \text{Hours for Sleeping}) \times 100\)%
Solution
For example, if Games is 45 degrees and Sleeping is 180 degrees, the calculations for hours would be: Games Hours = 45 / 15 = 3 hours Sleeping Hours = 180 / 15 = 12 hours
Then, the percentage is: \((3/12) \times 100 = 25\)%
Conclusion
The student spends 25% of the time on games in comparison to sleeping.
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Question: 3
If he spends the time in games equal to the home work and remains constant in other activities, then the percentage decrease in time of sleeping:
To solve the problem, we need to determine the percentage decrease in the time spent sleeping when the time spent playing games becomes equal to the time spent on homework, keeping other activities constant.
First, let's convert the angles in degrees into hours. The pie chart represents 360 degrees, and the total hours in a day is 24 hours. Therefore, each degree corresponds to:
\( \text{Hours per degree} = \frac{24 \text{ hours}}{360 \text{ degrees}} = \frac{1}{15} \text{ hours per degree} \)
Suppose the angle representing homework time is \( x \) degrees, then time spent on homework is:
If the time spent on games becomes equal to the time spent on homework, then the new time spent on games is also \( \frac{x}{15} \) hours, and the initial time represented by \( \text{games degrees} \), \( g \), is replaced with \( x \).
Since the time for other activities is constant, the time change comes from sleeping.
The decreased time in sleeping is equal to \( \frac{g-x}{15} \) hours.
To determine the difference in time spent at school and doing homework, follow these steps:
Understand the total degrees in a pie chart represent a full day, which equates to 24 hours.
Identify the degree measures corresponding to time spent at school and on homework from the pie chart. For this problem, you would typically have degree values such as \(x^\circ\) for school and \(y^\circ\) for homework.
Convert the degrees to hours for both activities using the equation: \( \text{hours} = \left( \frac{\text{degrees}}{360^\circ} \right) \times 24 \)
Once you have both times in hours, calculate the difference between the hours spent at school and on homework.
Given the task and understanding pie charts, suppose:
School is represented by \(180^\circ\).
Homework is represented by \(120^\circ\).
Now, carry out these conversions:
Time at school: \( \left( \frac{180^\circ}{360^\circ} \right) \times 24 = 12 \text{ hours} \)
Time on homework: \( \left( \frac{120^\circ}{360^\circ} \right) \times 24 = 8 \text{ hours} \)
Calculate the difference:
Difference = \( 12 - 8 = 4 \text{ hours} \)
Thus, the correct answer is 4.
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Question: 5
If he spends \(\frac{1}{3}\) rd time of homework in Mathematics then the number of hours he spends in rest of the subjects in home work:
Given that he spends \(\frac{1}{3}\) of his homework time on Mathematics, we need to find out how many hours he spends on the rest of the subjects. From the pie chart, assume that the total homework time is defined by the portion of the chart dedicated to homework.
To solve this:
First, determine the total number of hours dedicated to homework from the pie chart.
Assume the pie chart indicates homework in degrees. With 24 hours in a day, each hour corresponds to \(\frac{360}{24} = 15\) degrees.
From the pie chart, if the angle for homework is \(x\) degrees, then the total homework time is \(\frac{x}{15}\) hours.
If he spends \(\frac{1}{3}\) of this time on Mathematics, the remaining time for other subjects is \(\frac{2}{3}\) of the total homework time.
Mathematically, if the total homework time is \(T\), then Mathematics time is \(\frac{1}{3}T\), and other subjects time is \(\frac{2}{3}T\).
Given the correct answer is 2 hours spent on other subjects, and assuming \(T\) is such that \(\frac{2}{3}T = 2\), solve for \(T\):
\(\frac{2}{3}T = 2\)
Multiply both sides by \(\frac{3}{2}\) to solve for \(T\):
\(T = 2 \times \frac{3}{2} = 3\) hours
Thus, the total homework time is 3 hours, of which 1 hour is spent on Mathematics and 2 hours are spent on the rest, which matches the given correct option.
