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<H2>Solved problems on average age</H2> <H3>Problem 1</H3>The average age of boys in a class of 30 is 15 years. If 10 more boys join the class, the average of the whole class gets reduced by a year. What is the average age of newcomers? <B>Solution 1</B> <pre> Since the average age of boys in a class of 30 is 15 years, the sum of their ages is 30*15 = 450 years. Let N be the average age of 10 newcomers. Then the sum of their ages is 10N. The total sum of 30 + 10 boys is 450 + 10N, and their average age is {{{(450+10N)/(30+10)}}}. So, from the condition you have this equation {{{(450+10N)/40}}} = (15-1) = 14. Then 450 + 10N = 14*40 = 560. Hence, 10N = 560 - 450 = 110, which implies N = {{{110/10}}} = 11. <U>Answer</U>. The average age of newcomers is 11 years. <U>Check</U>. {{{(30*15 + 11*10)/40}}} = 14. ! Correct ! </pre> <H3>Problem 2</H3>Three years ago the average age of a family of six members was 19 years. A baby having been born, the average age of the family is same today. What is the age of baby. <B>Solution</B> <pre> Since average = total/n, the sum of ages of the six members 3 years ago was 19*6 = 114 years It implies that the sum of ages of the same six members NOW is 114 + 6*3 = 114 + 18 = 132 years. From the other side, the average of the SEVEN members of the family today is the same 19 yeras; hence, the sum of ages of the seven is 19*7 = 133 years. It implies that the age of the baby is 133 - 132 = 1 year. </pre> My other lessons on <B>Average, Mean and Median</B> in this site are - <A HREF=https://www.algebra.com/algebra/homework/Average/Geometric-Mean.lesson>WHAT IS Geometric mean</A> - <A HREF=https://www.algebra.com/algebra/homework/Average/Difference-between-Amean-and-Gmean.lesson>Difference between Arithmetic mean and Geometric mean</A> - <A HREF=https://www.algebra.com/algebra/homework/Average/What-is-Median.lesson>WHAT IS Median</A> - <A HREF=https://www.algebra.com/algebra/homework/Average/Solved-problems-on-average-scores-weight-height-and-temperature.lesson>Solved problems on average scores, weight, height and temperature</A> - <A HREF=https://www.algebra.com/algebra/homework/Average/Solved-problems-on-average-scores.lesson>Solved problems on average scores</A> - <A HREF=https://www.algebra.com/algebra/homework/Average/Miscellaneous-problems-on-average-values.lesson>Miscellaneous problems on average values</A> - <A HREF=https://www.algebra.com/algebra/homework/Average/Math-circle-level-problem-on-average.lesson>Math circle level problem on average</A> - <A HREF=https://www.algebra.com/algebra/homework/Average/Entertainment-problems-on-average.lesson>Entertainment problems on average</A> - <A HREF=https://www.algebra.com/algebra/homework/Average/The-mean-and-the-total-value-problem-for-the-International-Fools-day-of-April-1.lesson>The mean and the total value problem for the International Fools' day of April, 1</A> - <A HREF=https://www.algebra.com/algebra/homework/Average/OVERVIEW-of-lessons-on-Average-Mean-and-Median.lesson>OVERVIEW of lessons on Average</A>
