Family Age Ratio Calculation Explained
This problem involves finding the age of the oldest family member using the average age and the ratio of their ages. We need to calculate the total age first and then use the ratio to determine individual ages.
Understanding Average Age
The average age is calculated by dividing the sum of all ages by the number of people. The formula is:
Average Age = \(\frac{\text{Total Age}}{\text{Number of Members}}\)
From this, we can find the Total Age:
Total Age = Average Age \(\times\) Number of Members
Calculating Total Family Age
Given:
- Number of members = 4
- Average age = 35 years
Using the formula:
Total Age = \(35 \text{ years} \times 4\)
Total Age = \(140\) years
Breaking Down the Age Ratio
The ages of the 4 family members are in the ratio 8:7:1:12. This means their ages can be represented as multiples of some common factor, let's call it '$x$'.
- Age 1 = \(8x\)
- Age 2 = \(7x\)
- Age 3 = \(1x\)
- Age 4 = \(12x\)
The sum of the parts in the ratio is:
\(8 + 7 + 1 + 12 = 28\) parts
Determining Member Ages Step-by-Step
The sum of the individual ages must equal the Total Age we calculated.
- Set up the equation using the ratio parts and the total age:
\(8x + 7x + 1x + 12x = 140\)
- Combine the terms with '$x$':
\(28x = 140\)
- Solve for '$x$' by dividing the total age by the sum of the ratio parts:
\(x = \frac{140}{28}\)
\(x = 5\)
Finding the Oldest Member's Age
To find the age of the oldest member, we look for the largest number in the ratio, which is 12. The oldest member's age is represented by \(12x\).
- Oldest Member's Age = \(12x\)
- Substitute the value of '$x$' we found: Age = \(12 \times 5\)
- Oldest Member's Age = \(60\) years
Therefore, the age of the oldest member of the family is 60 years.
Similar Questions
- Four years ago, the ratio of the ages of A and B was 3: 5. Six years hence, the ratio of the ages of A and B will be 2: 3. What is the sum (in years) of the present ages of A and B?
The ages of A and B are in the ratio 4: 7, respectively. After 8 years, the ratio of their ages will be 2: 3. What is the sum of the ages of A and B (in years)?
The present ages of Ramu and Ravi are in the ratio of 4: 3. After 5 years the ratio of their ages will be 5: 4. Find their present ages, respectively.
- Six years ago, the average of the ages of Ravi, his wife and their child was 32 years. Nine years ago, the average of the ages of Ravi's wife and the child was 24 years. Find the present age of Ravi?
Important Questions from Problem on Age
The ratio of present ages of Neelam and Rajni is 6 : 7. After four years, their ages will be in the ratio of 8 : 9. What is the present age of Rajni?
Five years ago the age of the son was one third of that of his mother at that time. If the sum of their present ages is 70 years, then find the present age of the mother.
Jaya is 36 years old and her son Bharat is 11 years old. In how many years will Jaya be twice as Bharat's age?
The ratio of a father's age to his son's age is 3 ∶ 2 The product of the numbers representing their age is 486. The ratio of their ages after 5 years will be:
X said to Y, "At the time of your birth I was twice as old as you are at present." If the present age of X is 42 years, then consider the following statements:
1. 8 years ago, the age of X was five times the age of Y.
2. After 14 years, the age of X would be two times the age of Y.
Which of the above statements is/are correct?
