Problem 1 :
The sum of the age of a man and his son is 35 years and the
product of their ages is 150. Find their ages.
Solution :
Let x and y be the age of a man and his son respectively.
Sum of the age of a man and his son is 35
x + y = 35
y = 35 – x ------ (1)
Product of their ages is 150.
x ⋅ y = 150 ---- (2)
By applying the value of y in (2), we get
x(35 – x) = 150
35x – x2 = 150
x - 35x + 150 = 0
x2 - 30x – 5x + 150 = 0
(x – 5) (x - 30) = 0
x - 5 = 0 x = 5 |
x - 30 = 0 x = 30 |
Here x represent the man’s age. So it should not be 5.
y = 35 – 30
y = 5
Therefore the age of the man is 35 and his son is 5.
Problem 2 :
The product of the man’s age 5 years ago and 5 years later is 600. Find his present age.
Solution :
Let x be the present age of man
Age of man 5 years ago = (x – 5)
Age of man 5 years after = (x + 5)
The product of the man’s age 5 years ago and 5 years later is 600
(x – 5) (x + 5) = 600
x2 – 52 = 600
x2 – 25 = 600
x2 = 600 + 25
x2 = 625
x = √625
x = 25
Therefore the present age of the man is 25 years.
Problem 3 :
1 year ago a father was 8 times as old as his son. Now his age is square of his son’s age. Find the present age.
Solution :
Here the age of father is compared by his son age.
So x and y be the ages of his father and son
One year ago his father’s age = x – 1
(x - 1) = 8(y – 1) ----- (1)
x = y² ------ (2)
By applying (2) in (1), we get
y2 - 8y – 1 + 8 = 0
y2 - 8y + 7 = 0
(y - 1) (y – 7) = 0
y - 1 = 0 y = 1 If y = 1 x = 1² x = 1 |
y - 7 = 0 y = 7 If y = 7 x = 72 x = 49 |
Therefore the present age of father and son are 49 years and 7 years respectively.
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