Question

The Average age of four members of a family is decreased by 14 years, when an elder person in the family died and a baby was born. What was the age of the person who died?​

Answer 1

Answer:

56

Step-by-step explanation:

4multiplied by 14 gives56

Answer 2

Answer:

The age of the person who died = 56

Step-by-step explanation:

Given,

The Average age of four members of a family is decreased by 14 years when an elder person in the family died and a baby was born

To find,

The age of the person who died

Recall the formula

Average = $\frac{Sum\ of\ observations}{Total \ number\ of \ observations}$

Solution:

Let A be the average age of the family initially and 'x' be the age of the person who died

We have Average = $\frac{Total \ age}{number\ of\ persons}$

Since the average age of the 4 people initially = A, we have

Total age of 4 people initially  = Average age ×Number of people in the family

= A ×4

= 4A

Total age of 4 people initially = 4A

When an elder person died and a baby was born

Total number of people in the family now = 4

Since the age of the person who died is 'x', the total age of the family = Total age of initially - x

Since the total age of people in the family is 4A, we have

4A - x

Since it is given that, the average is decreased by 14 years, we have

the new average = A -14

A - 14 = $\frac{4A - x}{4}$

4(A - 14) = 4A -x

4A - 56 = 4A -x

x = 56

∴ The age of the person who died = 56

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