Question

5 years ago the age of man was 3years more than 4 times his son age after 3years the man will be 6 years less than thrice age of his son after how many years will sum of their ages be 80 years

Answer 1

Answer:

16 years

Step-by-step explanation:

Let the present ages of the man and his son be x and y respectively

5 years ago the age of the man = x-5

5 years ago, the age of the son = y-5

According to the question

x-5 = 4(y-5) +3

⇒ x = 4y - 20 + 3 +5

⇒ x - 4y = -12            ............... (1)

After 3 years, the age of the man = 3+x

After 3 years, the age of the son = 3+y

Again as per question

3+x = 3(y+3) - 6

⇒ x = 3y + 9 - 6 -3

⇒ x - 3y = 0            ............... (2)

Subtracting eq (1) from eq (2)

we get

y = 12

Putting the value of 12 in eq (2)

x = 36

Therefore, present age of man = 36 years and present age of son = 12 years

Let in z number of years, the sum of their ages will be will be 80

Then,

(36+z) + (12+z) = 80

⇒ 48 +2z = 80

⇒ 2z = 80 - 48

⇒ 2z = 80 - 48

⇒ 2z = 32

⇒ z = 16

Therefore in 16 years, the sum of their ages will be 80 years.