Question

ashok's age x years ago was twice his son’s age at that time. his age 5x years ago was thrice his sons age at that time. the difference of their present ages is 24 years. find the sum of their present ages. (in years)

Answer 1

Son’s age = y

Son's age x years ago = y – x

David's age x years ago=2(y − x) = 2y − 2x

Hence David's current age = 2y − 2x + x = 2y – x ……. (1)

Son's age 5x years ago = y − 5x

David's age 5x years ago =3(y − 5x) = 3y − 15x

So from this equation David's current age = 3y − 15x + 5x = 3y − 10x  ……….(2)

equating (1) & (2)

3y – 10x = 2y – x

y = 9x

Hence David's current age =2y – x = 2(9x) – x = 17x

Difference of their current ages =17x – 9x = 24

8x = 24

x=3

Hence current age of Son =9 x 3 = 27

David=17 x 3=51

So Sum of current ages = 27 + 51 = 78

Answer 2

Answer:

The sum of their present ages is 78 years.

Step-by-step explanation:

Let present age of Ashok be a years

It is given that difference of their present age is 24.

So,his present age is $(a - 24)$years.

x years ago, Ashok's age $= (a - x)$ years and his son's age $= (a - 24 - x)$years

It is given that Ashok's age x years ago was twice his son.

According to question,

$a - x = 2 \times (a - 24 - x) \\ a - x = 2a - 48 - 2x \\ a - x - 2a + 2x = - 48 \\ x - a = - 48....(1)$

5x years ago,Ashok's age =$(a - 5x)$years.and his son's age

$= (a - 24 - 5x)$years.

Again it is given that his age 5x years ago was thrice his sons age at that time.

$a - 5x = 3 \times (a - 24 - 5x) \\ a - 5x = 3a - 72 - 15x \\ a - 3a - 5x + 15x = - 72 \\ - 2a + 10x = - 72.....(2)$

From equation (1),

$x - a = - 48 \\ x = - 48 + a.....(3)$

We are putting value of x in equation (2),

$- 2a + 10( - 48 + a) = - 72 \\ - 2a - 480 + 10a = - 72 \\ 8a = - 72 + 480 \\ 8a = 408 \\ a = \frac{408}{8} \\ a = 51$

From equation (3),

$x = - 48 + 51 = 3$

So, present age of Ashok is 51 years and his son's age $(51 - 24) = 27$years.

Therefore sum of their present age $(51 + 27) = 78$years.