Calculating Past Average Family Age
The problem asks for the average age of the family members 5 years ago, just before the youngest member was born.
Step 1: Calculate the Current Total Age
The current family has 5 members, and their average age is 20 years.
Current Total Age = Number of Members \(\times\) Average Age
Current Total Age = \(5 \times 20 = 100\) years.
Step 2: Calculate the Total Age 5 Years Ago
Five years ago, the youngest member was not yet born. So, there were \(5 - 1 = 4\) members in the family.
Also, each of the 5 current members was 5 years younger.
Total reduction in age for all 5 members = Number of Members \(\times\) 5 years
Total reduction = \(5 \times 5 = 25\) years.
Total Age 5 Years Ago = Current Total Age - Total Reduction
Total Age 5 Years Ago = \(100 - 25 = 75\) years.
Step 3: Calculate the Average Age 5 Years Ago
The number of family members 5 years ago was 4.
Average Age 5 Years Ago = Total Age 5 Years Ago / Number of Members 5 Years Ago
Average Age 5 Years Ago = \(\frac{75}{4}\)
Average Age 5 Years Ago = \(18.75\) years.
Therefore, the average age of the family just before the birth of the youngest member was 18.75 years.
Important Questions from Age
The ages of two persons P and Q are in the ratio 5 : 7. Eight years ago, the ratio of P and Q was 7 : 13. The present ages of P and Q, respectively, are:
One year ago, the ratio of the ages of A and B was 4 : 3. The ratio of their ages, after 7 years from now, will be 9 : 7. What is the present age (in years) of B?
In 8 years, Subhash will be 3 times as old as he is now. After how many years will Subhash be 5 times as old as he is now?
The average ages of parents and two children are 30 years and 8 years respectively. The average age of the family is
A. 16 years
B. 19 years
C. 18 years
D. 17 years
A father is presently 3 times his daughter’s age. After 10 years he will be twice as old as her. Find the daughter’s present age.
