hello guys pls explain this question clearly
The sum of the ages of anup and his father is 100.Anup is as old as his father now, he will be five times as old as his son anuj is now.anuj will be eight years older than anup is now, when anup is as old as his father.what are their ages now?
Answers
Answer :- Anup age is 35 year, father age is 65 years and Anuj age is 43 years.
Explanation :-
Let the present age of Anup be x years and his father age be (100 - x) years.
The age of Anuj will be (100 - x)/5 years.
According to given conditions we get,
When Anup is as old as his father = (100 – 2x) years,
Anuj age = (100–x)/5+(100–2x) years
= 600–11x/5
Anuj age = x + 8
Now,
600–11x5 = x + 8
600 – 11x = 5x + 40
16x = 560
x = 560/60
x = 35 years
Therefore, Anup age = 35 years
Anup father age
= 100 – x
= 100 – 35
= 65 years
Anuj age = x + 8
= 35 + 8
= 43 years
Therefore, Anup age is 35 year, father age is 65 years and Anuj age is 43 years.
Answer:
Present age of Anup = 35 years
Age of his father = 65 years
Age of Anuj = 13 years
Step-by-step explanation:
Let the present ages of Anup, his father and his son Anuj be x, y and z respectively.
According to question, sum of ages of Anup and his father is 100 ⇒ x+y=100 .....(1)
Let their new ages after few years be x', y' and z' respectively.
After those few years, New age of Anup = Present age of father = 5 × Present age of Anuj
⇒x =y=5z .....(2)
Also, New age of Anuj= 8+Present age of Anup
⇒z =8+x .....(3)
∵ No. of years = New age - present age for each person
∴ No. of years =x−x=y −y=z −z
Taking first and last term we have,
x −x=z −z⇒y−(100−y)=(8+x)− 5y {Substituting values from equations (1),(2) and (3)}
⇒2y−100=8+x− 5y
⇒2y+ 5y−x=8+100⇒ 511y −x=108 ....(4)
Now adding the equations (1) and (4),
511y −x=108 y+x=100
5+16y =208 ⇒y=65
Now, from equation (1) , x=100−y=100−65=35
And from equation (2), z= 5y = 5
65 =13
Thus, Present age of Anup = 35 years
Age of his father = 65 years
Age of Anuj = 13 years