Question

T5) The average age of father, mother, son and
daughter is 16 years. Father is 5 times as old as the son
and mother is 6 times as old as the daughter. After 3
years from now, mother will be thrice as old as the son.
What is the present age of the father?​

Answer 1

Given:

The average age of father, mother, son and daughter is 16 years.

Father is 5 times as old as the son and mother is 6 times as old as the daughter.

After 3 years from now, mother will be thrice as old as the son.

To find:

What is the present age of the father?​

Solution:

We know,

$\boxed{\bold{Average = \frac{Sum \:of\: observations}{No. \:of\: observations} }}$

Let "F", "M", "S" & "D" be the present ages of the father, mother, son and daughter respectively.

The average age of father, mother, son and daughter is 16 years.

So, $\frac{F + M + S + D}{4} = 16$

$\implies F + M + S + D = 64$ ↔ Equation1

Father is 5 times as old as the son

i.e., $F = 5 S$ ↔ Equation2

Mother is 6 times as old as the daughter

i.e., $M = 6D$ ↔ Equation3

After 3 years from now, mother will be thrice as old as the son

i.e., $M + 3 = 3 (S + 3)$

$\implies M + 3 = 3S + 9$

$\implies M = 3S + 6$ ↔ Equation4

On substituting equation4 in equation3, we get

$3S + 6 = 6D$

$\implies D = \frac{S + 2 }{2}$ ↔ equation5

Now, on substituting equation2, 4 and 5 in equation1, we get

$\implies 5 S+ 3S + 6 + S + \frac{S + 2 }{2} = 64$

$\implies \frac{10S + 6S + 12 + 2S + S + 2}{2} = 64$

$\implies 19S + 14 = 128$

$\implies 19S = 114$

$\implies S = 6$

∴ $F = 5S = 5 \times 6 = 30\:years$

Thus, the present age pf the father is → 30 years.

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