anand is 5 years older than his sister anju, their father is 20 years older than anand. 4 years ago the father age was twice the sum of anand and anju. find their present age
Answers
Their present age is:
Anju = 9 years
Anand = 14 years
Father = 34 years
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Let's now solve the given problem:
Let's say,
"x" → represents the present age of Anju
"y" → represents the present age of Anand
"z" → represents the present age of Father
Anand is 5 years older than his sister Anju, so we can form the equation as,
y = x + 5 . . . (1)
Their father is 20 years older than Anand, so we can form the equation as,
z = y + 20
on substituting from (1), we get
⇒ z = x + 5 + 20
⇒ z = x + 25 . . . (2)
4 years ago:
Anju's age = x - 4
Anand's age = y - 4
Father's age = z - 4
4 years ago the father age was twice the sum of Anand and Anju, so we can form the equation as,
z - 4 = 2[(y - 4) + (x - 4)]
on substituting from (1) and (2), we get
⇒ x + 25 - 4 = 2[(x + 5 - 4) + (x - 4)]
⇒ x + 21 = 2[(x + 1) + (x - 4)]
⇒ x + 21 = 2[x + x - 3]
⇒ x + 21 = 2[2x - 3]
⇒ x + 21 = 4x - 6
⇒ 4x - x = 21 + 6
⇒ 3x = 27
⇒ x = 9 years ← Anju's present age
∴ Anand's present age = x + 5 = 9 + 5 = 14 years
∴ Theire father's present age = x + 25 = 9 + 25 = 34 years
Thus, the present age of Anju is 9 years, Anand is 14 years and their father's is 34 years.
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