the sum of the ages of anup and his father is 100.when anup is as old as his farther now,he will be 5 times as old as his son anuj. anuj will be 8 years older than anup is now, when anup is as old as his father.what are their ages now?
Answers
Answer:
Step-by-step explanation:
Let Anup's age be A and Anup's father's age = F. Then A + F = 100.
Father's age F = 100 - A.
When Anup is as old as his father, his age will be (100 - A).
Difference between Anup's age now and then = (100 - A) - A = (100 - 2A).
Hence Anup will reach his father's age after (100 - 2A) years.
Anuj's age now = (1/5) of Anup's age when his age equals his father's age = (100 - A)/5.
Anuj's age when Anup attains his father's age,i.e., after (100 - 2A) Years = [(100 - A)/5] + (100 - 2A).
This age is 8 years more than Anup's age now,i.e., 8 more than A = A + 8.
Hence [(100 - A)/5] + (100 - 2A) = A + 8
Solving, Anup's age A = 35, Anup's father's age F = 65, Anuj's age = (100 - 35)/5 = 13.
• Let present age of Anup he (x) years, present age of father be (y) years and Anuj be (z) years.
_________ [ ASSUME ]
We have to find the present age of Anup (x), father (y) and Anuj (z).
_________________ [FIND ]
» The sum of the ages of anup and his father is 100.
→ x + y = 100
→ x = 100 - y _________ (eq 1)
» He will be 5 times as old as his son Anuj.
A.T.Q.
→ y = 5(z)
→ y = 5z ________ (eq 2)
Put value of N in (eq 1)
→ x = 100 - 5z _______ (eq 3)
» Anuj will be 8 years older than anup is now, when anup is as old as his father.
A.T.Q.
→ z + y - a = 8 + x
→ z + y = 8 + x + x
→ z + y = 8 + 2x
→ z + 5z = 8 + 2x [From (eq 2)]
→ 6z = 8 + 2x
→ 3z = 4 + x
→ 3z = 4 + 100 - 5z [From (eq 3)]
→ 3z + 5z = 104
→ 8z = 104
- z = 13 (age of Anuj)
Put value of z in (eq 3)
→ x = 100 - 5(13)
→ x = 100 - 65
- x = 35 (age of Anup)
Also, put value of z in (eq 2)
→ y = 5(13)
- y = 65 (age of father)
_____________________________
Age of Anup (x) = 35 years.
Age of Father (y) = 65 years.
Age of Anuj (z) = 13 years.
________ [ ANSWER ]
____________________________