Finding Kishore's Present Age

This problem requires us to use the concept of average age and how ages change over time to determine Kishore's current age.

The average age of a group is the sum of the ages of all members divided by the number of members. Conversely, the sum of ages is the average age multiplied by the number of members.

Step 1: Calculate the Sum of Ages for Kishore, Wife, and Child 6 Years Ago

We are given that the average age of Kishore, his wife, and their child 6 years ago was 38 years.

• Number of people = 3 (Kishore, Wife, Child)
• Average age 6 years ago = 38 years
• Sum of ages 6 years ago = Average age $\times$ Number of people

Sum of ages 6 years ago = $38 \times 3$ years

$$38 \times 3 = 114$$

So, the sum of their ages 6 years ago was 114 years.

Step 2: Calculate the Present Sum of Ages for Kishore, Wife, and Child

To find the present sum of their ages, we need to account for the 6 years that have passed. Each person's age has increased by 6 years.

• Number of people = 3
• Time passed = 6 years
• Total increase in age = Number of people $\times$ Time passed

Total increase in age = $3 \times 6$ years

$$3 \times 6 = 18$$

Present sum of ages = Sum of ages 6 years ago + Total increase in age

Present sum of ages = $114 + 18$ years

$$114 + 18 = 132$$

Let Kishore's present age be K, his wife's present age be W, and their child's present age be C.

So, we have the equation: K + W + C = 132 (Equation 1)

Step 3: Calculate the Sum of Ages for Wife and Child 8 Years Ago

We are given that the average age of Kishore's wife and their child 8 years ago was 32 years.

• Number of people = 2 (Wife, Child)
• Average age 8 years ago = 32 years
• Sum of ages 8 years ago = Average age $\times$ Number of people

Sum of ages 8 years ago = $32 \times 2$ years

$$32 \times 2 = 64$$

So, the sum of the wife's and child's ages 8 years ago was 64 years.

Step 4: Calculate the Present Sum of Ages for Wife and Child

To find the present sum of their ages, we need to account for the 8 years that have passed. Each person's age has increased by 8 years.

• Number of people = 2
• Time passed = 8 years
• Total increase in age = Number of people $\times$ Time passed

Total increase in age = $2 \times 8$ years

$$2 \times 8 = 16$$

Present sum of ages (Wife and Child) = Sum of ages 8 years ago + Total increase in age

Present sum of ages (Wife and Child) = $64 + 16$ years

$$64 + 16 = 80$$

So, we have the equation: W + C = 80 (Equation 2)

Step 5: Find Kishore's Present Age

We have two equations:

1. K + W + C = 132
2. W + C = 80

We can substitute the value of (W + C) from Equation 2 into Equation 1:

K + (W + C) = 132

K + 80 = 132

Now, solve for K:

K = 132 - 80

$$K = 52$$

Therefore, Kishore's present age is 52 years.

Summary of Calculations

Using the present sums: (K + W + C) - (W + C) = K

$132 - 80 = 52$ years

Kishore's present age is 52 years.

Revision Table: Key Age Calculation Concepts

Additional Information on Age Problems

Age problems are common in quantitative aptitude and involve using relationships between people's ages at different points in time. Here are some additional points to remember:

• The difference between two people's ages remains constant throughout their lives.
• If the sum of ages of N people T years ago was S, their present sum of ages is $S + N \times T$.
• If the sum of ages of N people is S, their sum of ages T years from now will be $S + N \times T$.
• Always be careful with the timeline – distinguish between past, present, and future ages.
• Set up variables for the present ages (or ages at a specific reference point) and form equations based on the given information.

Practicing different types of age problems helps in understanding the application of these concepts.