Class 10 Exam > Class 10 Questions > The minimum age of a children to be eligible ...
Start Learning for Free
The minimum age of a children to be eligible to participate in a painting competition in 8 years it is observed that the age of youngest boy was 8 years and the ages of a rest of participant are having a common difference of 4 months if the sum of Ages of all the participant 168 years , find the age of eldest participate in the painting competition.?
Most Upvoted Answer
The minimum age of a children to be eligible to participate in a paint...
Community Answer
The minimum age of a children to be eligible to participate in a paint...
Given information:
- The age of the youngest boy is 8 years.
- The ages of the rest of the participants have a common difference of 4 months.
- The sum of the ages of all the participants is 168 years.
Calculating the number of participants:
To find the age of the eldest participant, we first need to determine how many participants there are in total. We can do this by finding the common difference of the ages and calculating the number of terms in the arithmetic sequence.
Let's assume the number of participants is 'n' (including the youngest boy). The age of the youngest boy is 8 years, so the second participant would be 8 + 4 months, the third participant would be 8 + 8 months, and so on.
We can represent the ages of the participants as an arithmetic sequence:
8, 8 + 4 months, 8 + 8 months, 8 + 12 months, ...
The nth term of an arithmetic sequence can be found using the formula:
an = a + (n - 1)d
In this case, a = 8 years (or 96 months) and d = 4 months. We need to find the value of n when the sum of the ages of all participants is 168 years (or 2016 months).
Calculating the sum of ages:
The sum of an arithmetic sequence can be calculated using the formula:
Sn = (n/2)(2a + (n - 1)d)
In this case, the sum of the ages is given as 168 years (or 2016 months). Plugging in the values, we have:
2016 = (n/2)(2*96 + (n - 1)*4)
Simplifying the equation:
2016 = (n/2)(192 + 4n - 4)
2016 = (n/2)(188 + 4n)
4032 = n(188 + 4n)
Simplifying further, we get a quadratic equation:
4n^2 + 188n - 4032 = 0
Solving the quadratic equation:
Using the quadratic formula:
n = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 4, b = 188, and c = -4032. Plugging in the values, we can solve for n.
After calculating, we find that n = 9 or n = -47/2. Since the number of participants cannot be negative, we discard the negative value.
Therefore, there are 9 participants in total, including the youngest boy.
Calculating the age of the eldest participant:
Now that we know there are 9 participants, we can find the age of the eldest participant by adding the common difference to the age of the youngest boy 8 times.
The age of the eldest participant = 8 years + 8 * 4 months
Converting months to years, we get:
8 + (8 * 4) / 12 = 10 and 2/3 years
Therefore, the age of the eldest participant in the painting competition is 10 years and 8 months.
- The age of the youngest boy is 8 years.
- The ages of the rest of the participants have a common difference of 4 months.
- The sum of the ages of all the participants is 168 years.
Calculating the number of participants:
To find the age of the eldest participant, we first need to determine how many participants there are in total. We can do this by finding the common difference of the ages and calculating the number of terms in the arithmetic sequence.
Let's assume the number of participants is 'n' (including the youngest boy). The age of the youngest boy is 8 years, so the second participant would be 8 + 4 months, the third participant would be 8 + 8 months, and so on.
We can represent the ages of the participants as an arithmetic sequence:
8, 8 + 4 months, 8 + 8 months, 8 + 12 months, ...
The nth term of an arithmetic sequence can be found using the formula:
an = a + (n - 1)d
In this case, a = 8 years (or 96 months) and d = 4 months. We need to find the value of n when the sum of the ages of all participants is 168 years (or 2016 months).
Calculating the sum of ages:
The sum of an arithmetic sequence can be calculated using the formula:
Sn = (n/2)(2a + (n - 1)d)
In this case, the sum of the ages is given as 168 years (or 2016 months). Plugging in the values, we have:
2016 = (n/2)(2*96 + (n - 1)*4)
Simplifying the equation:
2016 = (n/2)(192 + 4n - 4)
2016 = (n/2)(188 + 4n)
4032 = n(188 + 4n)
Simplifying further, we get a quadratic equation:
4n^2 + 188n - 4032 = 0
Solving the quadratic equation:
Using the quadratic formula:
n = (-b ± √(b^2 - 4ac)) / 2a
In this case, a = 4, b = 188, and c = -4032. Plugging in the values, we can solve for n.
After calculating, we find that n = 9 or n = -47/2. Since the number of participants cannot be negative, we discard the negative value.
Therefore, there are 9 participants in total, including the youngest boy.
Calculating the age of the eldest participant:
Now that we know there are 9 participants, we can find the age of the eldest participant by adding the common difference to the age of the youngest boy 8 times.
The age of the eldest participant = 8 years + 8 * 4 months
Converting months to years, we get:
8 + (8 * 4) / 12 = 10 and 2/3 years
Therefore, the age of the eldest participant in the painting competition is 10 years and 8 months.
Attention Class 10 Students!
To make sure you are not studying endlessly, EduRev has designed Class 10 study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in Class 10.
|
Explore Courses for Class 10 exam
|
|
Similar Class 10 Doubts
Top Courses for Class 10View all
The minimum age of a children to be eligible to participate in a painting competition in 8 years it is observed that the age of youngest boy was 8 years and the ages of a rest of participant are having a common difference of 4 months if the sum of Ages of all the participant 168 years , find the age of eldest participate in the painting competition.?
Question Description
The minimum age of a children to be eligible to participate in a painting competition in 8 years it is observed that the age of youngest boy was 8 years and the ages of a rest of participant are having a common difference of 4 months if the sum of Ages of all the participant 168 years , find the age of eldest participate in the painting competition.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The minimum age of a children to be eligible to participate in a painting competition in 8 years it is observed that the age of youngest boy was 8 years and the ages of a rest of participant are having a common difference of 4 months if the sum of Ages of all the participant 168 years , find the age of eldest participate in the painting competition.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The minimum age of a children to be eligible to participate in a painting competition in 8 years it is observed that the age of youngest boy was 8 years and the ages of a rest of participant are having a common difference of 4 months if the sum of Ages of all the participant 168 years , find the age of eldest participate in the painting competition.?.
The minimum age of a children to be eligible to participate in a painting competition in 8 years it is observed that the age of youngest boy was 8 years and the ages of a rest of participant are having a common difference of 4 months if the sum of Ages of all the participant 168 years , find the age of eldest participate in the painting competition.? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The minimum age of a children to be eligible to participate in a painting competition in 8 years it is observed that the age of youngest boy was 8 years and the ages of a rest of participant are having a common difference of 4 months if the sum of Ages of all the participant 168 years , find the age of eldest participate in the painting competition.? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The minimum age of a children to be eligible to participate in a painting competition in 8 years it is observed that the age of youngest boy was 8 years and the ages of a rest of participant are having a common difference of 4 months if the sum of Ages of all the participant 168 years , find the age of eldest participate in the painting competition.?.
Solutions for The minimum age of a children to be eligible to participate in a painting competition in 8 years it is observed that the age of youngest boy was 8 years and the ages of a rest of participant are having a common difference of 4 months if the sum of Ages of all the participant 168 years , find the age of eldest participate in the painting competition.? in English & in Hindi are available as part of our courses for Class 10.
Download more important topics, notes, lectures and mock test series for Class 10 Exam by signing up for free.
Here you can find the meaning of The minimum age of a children to be eligible to participate in a painting competition in 8 years it is observed that the age of youngest boy was 8 years and the ages of a rest of participant are having a common difference of 4 months if the sum of Ages of all the participant 168 years , find the age of eldest participate in the painting competition.? defined & explained in the simplest way possible. Besides giving the explanation of
The minimum age of a children to be eligible to participate in a painting competition in 8 years it is observed that the age of youngest boy was 8 years and the ages of a rest of participant are having a common difference of 4 months if the sum of Ages of all the participant 168 years , find the age of eldest participate in the painting competition.?, a detailed solution for The minimum age of a children to be eligible to participate in a painting competition in 8 years it is observed that the age of youngest boy was 8 years and the ages of a rest of participant are having a common difference of 4 months if the sum of Ages of all the participant 168 years , find the age of eldest participate in the painting competition.? has been provided alongside types of The minimum age of a children to be eligible to participate in a painting competition in 8 years it is observed that the age of youngest boy was 8 years and the ages of a rest of participant are having a common difference of 4 months if the sum of Ages of all the participant 168 years , find the age of eldest participate in the painting competition.? theory, EduRev gives you an
ample number of questions to practice The minimum age of a children to be eligible to participate in a painting competition in 8 years it is observed that the age of youngest boy was 8 years and the ages of a rest of participant are having a common difference of 4 months if the sum of Ages of all the participant 168 years , find the age of eldest participate in the painting competition.? tests, examples and also practice Class 10 tests.
|
|
Explore Courses for Class 10 exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup