Question

6 years ago, Mr. X was 5 times the age of his son Y. After 6 years, Mr.X will be thrice the age of his son.
What is the present age of the X?
Correct answer: +1
Incorrect answer: 0
Options
52 years
66 years
50 years
-45 years
None of these​

Answer 1

Given :

• 6 years ago, Mr. X was 5 times the age of his son Y.

• After 6 years, Mr. X will be thrice the age of his son.

To find :

• Present age of X

Solution :

Let,

• Present age of Y = a years
• Present age of X = b years

Their ages 6 years :-

• X's age = b - 6 years
• Y's age = a - 6 years

According to the first condition given,

→ b - 6 = 5(a - 6)

→ b - 6 = 5a - 30

→ b - 5a = - 30 + 6

→ b - 5a = - 24

→ - (5a - b) = - 24

→ 5a - b = 24 ------(1)

Their ages after 6 years :-

• X's age = b + 6 years
• Y's age = a + 6 years

According to the second condition given,

→ b + 6 = 3(a + 6)

→ b + 6 = 3a + 18

→ - 3a + b = 18 - 6

→ - 3a + b = 12 -----(2)

Solving (1) and (2) :-

→ 5a - b = 24

→ -3a + b = 12

____________

→ 2a = 36

____________

→ 2a = 36

→ a = 36 ÷ 2

→ a = 18

Substitute the value of a in equation (1) :-

→ 5a - b = 24

→ 5(18) - b = 24

→ 90 - b = 24

→ - b = 24 - 90

→ - b = - 66

→ b = 66

Therefore, the age of X = 66 years