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
• Let present age of Anup he (A) years, present age of father be (F) years and Anuj be (J) years.
We have to find the present age of Anup (A), father (F) and Anuj (J).
» The sum of the ages of anup and his father is 100.
→ A + F = 100
→ A = 100 - F _________ (eq 1)
» He will be 5 times as old as his son Anuj.
A.T.Q.
→ F = 5(J)
→ F = 5J ________ (eq 2)
Put value of N in (eq 1)
→ A = 100 - 5J _______ (eq 3)
→ A + 5J = 100
» Anuj will be 8 years older than anup is now, when anup is as old as his father.
A.T.Q.
→ J + F - M = 8 + A
→ J + F = 8 + A + A
→ J + F = 8 + 2A
→ J + 5J = 8 + 2A [From (eq 2)]
→ 6J = 8 + 2A
→ 3J = 4 + A
→ 3J = 4 + 100 - 5J [From (eq 3)]
→ 3J + 5J = 104
→ 8J = 104
→ J = 13 (age of Anuj)
Put value of J in (eq 3)
→ A = 100 - 5(13)
→ A = 100 - 65
→ A = 35 (age of Anup)
Also, put value of J in (eq 2)
→ F = 5(13)
→ F = 65 (age of father)
_____________________________
Age of Anup (A) = 35 years.
Age of Father (F) = 65 years.
Age of Anuj (J) = 13 years.
________ [ ANSWER ]
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