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The average age of a class of 25 students is 14 years. Some new students with an
average age of 13 years 6 months join the class, there by decreasing the average
by 1 month. Find the total strength at present.?
average age of 13 years 6 months join the class, there by decreasing the average
by 1 month. Find the total strength at present.?
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The average age of a class of 25 students is 14 years. Some new studen...
Given information:
- Average age of the class of 25 students = 14 years
- Average age of new students = 13 years 6 months
- Decrease in average age = 1 month
Let's solve the problem step by step:
Step 1: Finding the total age of the initial 25 students
Total age of 25 students = Average age * Total number of students
Total age of 25 students = 14 years * 25 = 350 years
Step 2: Finding the total age of the new students
Let the total number of new students be x.
Total age of new students = Average age * Total number of new students
Total age of new students = 13.5 years * x
Step 3: Finding the total age of all students after the new students join
Total age of all students = Total age of initial students + Total age of new students
Total age of all students = 350 + 13.5x
Step 4: Finding the new average age after the new students join
New average age = Total age of all students / Total number of students
New average age = (350 + 13.5x) / (25 + x)
Given that the new average age is 1 month less than the initial average age:
14 years - 1 month = (350 + 13.5x) / (25 + x)
Step 5: Solving the equation
13 years 11 months = (350 + 13.5x) / (25 + x)
Solving the above equation will give us the value of x, which represents the total number of new students. Adding this value to the initial total number of students (25) will give us the total strength of the class at present.
- Average age of the class of 25 students = 14 years
- Average age of new students = 13 years 6 months
- Decrease in average age = 1 month
Let's solve the problem step by step:
Step 1: Finding the total age of the initial 25 students
Total age of 25 students = Average age * Total number of students
Total age of 25 students = 14 years * 25 = 350 years
Step 2: Finding the total age of the new students
Let the total number of new students be x.
Total age of new students = Average age * Total number of new students
Total age of new students = 13.5 years * x
Step 3: Finding the total age of all students after the new students join
Total age of all students = Total age of initial students + Total age of new students
Total age of all students = 350 + 13.5x
Step 4: Finding the new average age after the new students join
New average age = Total age of all students / Total number of students
New average age = (350 + 13.5x) / (25 + x)
Given that the new average age is 1 month less than the initial average age:
14 years - 1 month = (350 + 13.5x) / (25 + x)
Step 5: Solving the equation
13 years 11 months = (350 + 13.5x) / (25 + x)
Solving the above equation will give us the value of x, which represents the total number of new students. Adding this value to the initial total number of students (25) will give us the total strength of the class at present.
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The average age of a class of 25 students is 14 years. Some new students with anaverage age of 13 years 6 months join the class, there by decreasing the averageby 1 month. Find the total strength at present.?
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