The average age of a family of three members (mother, father and Son) is 44 years. After the son's marriage, the average age of the family becomes 39 years. What is the age of the daughter-in-law?
24 years
Understanding the Family Average Age Problem
This question involves calculating the age of a new member added to a family based on the change in the family's average age. The average age is the sum of the ages of all members divided by the number of members.
Let's break down the information given:
- Initially, there are 3 family members (Mother, Father, Son).
- The average age of these 3 members is 44 years.
- After the son's marriage, a new member (Daughter-in-law) joins the family, making it 4 members.
- The new average age of the 4 members is 39 years.
Step-by-Step Solution for Calculating Age
To find the age of the daughter-in-law, we first need to calculate the total sum of ages in both scenarios.
Step 1: Calculate the initial total age of the family
The initial family has 3 members, and their average age is 44 years. The sum of their ages is calculated as:
Sum of ages = Average age $\times$ Number of members
Initial sum of ages $= 44 \text{ years} \times 3 = 132 \text{ years}$
So, the combined age of the Mother, Father, and Son is 132 years.
Step 2: Calculate the total age of the family after the son's marriage
After the son's marriage, the family has 4 members, and their average age is 39 years. The sum of their ages is calculated as:
Sum of ages = Average age $\times$ Number of members
Sum of ages after marriage $= 39 \text{ years} \times 4 = 156 \text{ years}$
So, the combined age of the Mother, Father, Son, and Daughter-in-law is 156 years.
Step 3: Calculate the age of the daughter-in-law
The difference between the total age of the family after the marriage and the initial total age is the age of the new member (the daughter-in-law).
Age of Daughter-in-law = Sum of ages after marriage - Initial sum of ages
Age of Daughter-in-law $= 156 \text{ years} - 132 \text{ years}$
Age of Daughter-in-law $= 24 \text{ years}$
Therefore, the age of the daughter-in-law is 24 years.
Summary of Calculations
| Scenario | Number of Members | Average Age (Years) | Total Age (Years) |
|---|---|---|---|
| Initial Family (M+F+S) | 3 | 44 | $44 \times 3 = 132$ |
| Family After Marriage (M+F+S+D) | 4 | 39 | $39 \times 4 = 156$ |
Age of Daughter-in-law = Total Age (After Marriage) - Total Age (Initial)
Age of Daughter-in-law = $156 - 132 = 24$ years.
Conclusion on Daughter-in-law's Age
Based on the calculations, the age of the daughter-in-law is 24 years. This matches option 1.
Revision Table: Family Age Problem
| Concept | Formula/Method | Application in this Problem |
|---|---|---|
| Average | Sum of values / Number of values | Given for initial family and family after marriage. |
| Total Sum | Average $\times$ Number of members | Used to find initial and final total age. |
| Finding Age of New Member | New Total Sum - Old Total Sum | Used to find the daughter-in-law's age. |
Additional Information: Average Calculation Tips
Understanding averages is fundamental in many quantitative problems. Here are some key points:
- The average represents a central value in a set of numbers.
- When a new member is added to a group, the average can change. If the new member's value (age in this case) is higher than the current average, the average increases. If it's lower, the average decreases. If it's equal, the average stays the same.
- In this problem, the average age decreased from 44 to 39 when the daughter-in-law joined. This implies the daughter-in-law's age must be less than the initial average age of 44. Let's verify: 24 is indeed less than 44.
- Calculating the total sum is often the first step when dealing with average problems involving changes in the number of members or the average itself.
Important Questions from Average
The average of 28 numbers is 77. The average of first 14 numbers is 74 and the average of last 15 numbers is 84. If the 14 th number is excluded, then what is the average of remaining numbers? (correct to one decimal places)
24 students collected money for donation. The average contribution was Rs. 50. Later on, their teacher also contributed some money. Now the average contribution is Rs. 56. The teacher’s contribution is:
Out of 6 numbers, the sum of the first 5 numbers is 7 times the 6 th number. If their average is 136, then the 6 th number is:
The average of five numbers is 30. If one number is excluded, then average becomes 31. What is the excluded number?
The average weight of 49 students in a class is 39 kg. Seven of them whose average weight is 40 kg leave the class and other seven students whose average weight is 54 kg join the class. What is the new average weight (in kg) of the class?
