Question

The average age of the members in a family decreased by two years when a person aged 52 years passed away. Instead, had a new baby been born in the family, the average age would have decreased by six years. Find the initial average age of all the members in the
family (In years). 0 32 0 36 O 39 O 42​

Answer 1

Answer:

Average - 42 Years

Step-by-step explanation:

Let average age be 'a' and number of members be 'n' then, sum of age of all the members will be 'na'.

Since,

Sum of Age/Number of Members = Average Age

=> Sum of Age / n = a => Sum of age = na

Given Information :

Case 1: na -52/n -1 = a -2 (equation 1)

Case 2: na + 0/n+1 = a - 6 (equation 2)

Solving Equation 1 and Equation 2:

2n + a = 54 (Solved Equation 1)

a - 6n = 6 (Solved Equation 2)

Now Solving the Equations for the value of 'a'

3a + 6n = 162 (Equation 1 multiplied by 3)

a - 6n = 6 (Equation 2)

Adding the above equations:

4a = 168 => a = 42 years

Answer 2

Answer:

$42$

Step-by-step explanation:

In the given question we have to assume two different variables $A$ and $F$ for the average age of the family and total family members in the family

As we know that

Average$=\frac{Sum of Observations}{Number of Observations}$

Thus present age sum of the family be $AF$

Now, according to the first condition in the question that the average age of the members in a family decreased by two years when a person aged 52 years passed away

The new Average of the family will be $A-2$

and total family members will be $F-1$

The sum of the ages of the remaining members in the family is $AF-52$

we also can say that

$A-2=\frac{AF-52}{F-1}$, on solving this equation we get

$(A-2)(F-1)=AF-52\\AF-2F-A+2=AF-52\\A+2F=54 (Equation 1)$

Now as per the second condition in the question that a new baby been born in the family, the average age would have decreased by six years,

The new Average of the family will be $A-6$

and total family members will be $F+1$

Now, the age of the newborn baby will remain $0$ (Zero)year

The total age of the family member will remain the same $AF$

As per the Average formula, we get that

$A-6=\frac{AF}{F+1}$ on solving this we get

$AF=(A-6)(F+1)\\AF=AF-6F+A-6\\A-6F-6=0\\A-6F=6 (Equation 2)$

From equation 1, we get the value of $F=\frac{54-A}{2 }$ substitute it in Equation 2

$A-6(\frac{54-A}{2})=6\\A-3(54-A)=6\\A-162+3A=6\\4A=168\\A=42$

Thus the initial average age of the family is $42$ years