Question

20 years ago when my parents got married their average age of my family with me and my parents is 34 years. What is my present age

Answer 1

Correct Question:-

20 years ago when my parents got married their average age and now average age of my family (parents) with me is 34 years. What is my present age?

Solution:-

Let the -

• the present age of father = x years
• preset age of mother = y years
• present age of son (me) = z years

$\underline{\underline{\sf{20\:years\:ago}}}$

→ Age of father = (x - 20) years

→ Age of mother = (y - 20) years

According to question,

Average age of father and mother is sum of their ages divide by 2.

$\implies\:\sf{\dfrac{x\:-\:20\:+\:y\:-\:20}{2}\:=\:34}$

$\implies\:\sf{\dfrac{x\:+\:y}{2}\:=\:34}$

$\implies\:\sf{x\:+\:y\:=\:68}$ ....(1)

Also, given that

Average ages of father, mother and son (me) is 34 years.

So, average of our ages is sum of our ages divide by 3. (As here we are talking about three persons. So, divide with 3)

$\implies\:\sf{\dfrac{x\:+\:y\:+\:z}{3}\:=\:34}$

$\implies\:\sf{x\:+\:y\:+\:z\:=\:102}$

$\implies\:\sf{68\:+\:+\:z\:=\:102}$ [From (1)]

$\implies\:\sf{z\:=\:34}$

•°• My present age is 34 years.

Answer 2

$\LARGE\underline{\underline{\sf Given:}}$

• 20years ago his parents married.

• Average age of family = 34years

$\LARGE\underline{\underline{\sf To\:Find:}}$

• His present age = ?

$\LARGE\underline{\underline{\sf Solution:}}$

Let ,

His present age is = x

His Mother age is = y

and His father age is = z

$\large\underline{\underline{\sf According\:to\: Question:}}$

20 years ago average age of father and mother is 34 years :

So ,

$\large\implies{\sf \dfrac{(z-20)+(y-20)}{2}=34 }$

$\large\implies{\sf \dfrac{z+y}{2}=34}$

$\large\implies{\sf z+y=68 }$

________________________________________

And ,

Average age of family (Father, Mother, Son) is given 34.

$\large\implies{\sf \dfrac{x+y+z}{3}=34}$

$\large\implies{\sf x+y+z=102 }$

$\large\implies{\sf 68+x=102 }$

$\large\implies{\sf x=102-68}$

$\large\implies{\sf x=34}$

_____________________________________

$\LARGE\underline{\underline{\sf Answer:}}$

•°• His present age is 34.