## SOLVING WORD PROBLEMS INVOLVING AGE

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  =  0x  =  5 x - 30  =  0x  =  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

x =  600 + 25

x =  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  =  0y  =  1If  y  =  1x  =  1²x  =  1 y - 7  =  0y  =  7If  y  =  7x  =  72x  =  49

Therefore the present age of father and son are 49 years and 7 years respectively.

Problem 4 :

The sum of the age of a father and his son is 45 years. Five years ago the product of their ages was 124. Determine their present age.

Solution :

Let x and y be the present age of father and his son respectively.

The sum of the age of a father and his son is 45 years.

x + y  =  45

y  =  45 – x  ------(1)

Five years ago his father’s age  =  x - 5

Five years ago son’s age  =  y – 5

Five years ago the product of their ages was 124.

(x – 5) (y – 5)  =  124

(x – 5) (45 – x – 5)  =  124

(x – 5) (40 – x)  =  124

40x – x2 – 200 + 5x  =  124

45x – x² – 200  =  124

x² – 45x + 124 + 200  =  0

x² – 45x + 324  =  0

(x – 9) (x – 36)  =  0

 x - 9  =  0x  =  9 x - 36  =  0x  =  36

Here x represent the present age of father. The possible age of father is 36.

To find the value of y, we may apply the value of x in (1), we get

y  =  45 - 36

y  =  9

Therefore the present age of father  =  36 years.

Present age of son  =  9 years.

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