# Algebra Age Problems

Application of word problems :

In this section,we shall learn Algebra age problems. For solving these, you have to remember some important points.

1) Read the problem carefully and note down what is given and what is required.
2) Denote the unknown by some letter such as x , y ,z etc.
3) Translate the statements of the problem into mathematical statements.
4) In Algebra age problems,first check whether they have given some years later or some years before. So accordingly you have to add or subtract the years given.

Algebra age problems contain the problems based on present age or some year hence.

Some solved examples on Algebra Age problems

1) The present age of Jacob’s father is three times that of Jacob. After 5 years, sum of their ages would be 70 years. Find their present ages.

Solution :
Let Jacob’s age = x years

His fathers’s age = 3x years

After 5 years

Jacob’s age = x + 5

Father’s age = 3x + 5

Sum of their age = 70

X + 5 + 3x + 5 = 70

4x + 10 = 70

4x = 60

X = 15

Jacob’s age = 15 years and his father’s age = 3(15) = 45 years

2) After 15 years, Ariel’s age will become four times that of her present age. Find her age.

Solution :
Let Ariel’s present age = x years

After 15 years, her age = x + 15

X + 15 = 4x

X – 4x = -15
-3x = -15

X = 5

Ariel’s present age = 5 years.

3) John’s mother’s age is 5 years more than the three times of John’s present age. Find John’s present age, if his mother is 44 years old.

Solution :
Let John’s age = x year

Then 3 x + 5 = 44

Or 3 x = 44 – 5 = 39

Or x = 13 years

John’s present age = 13 years.

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4) The present ages of Deklerk and Saniya are in the ratio 3:4. Five years from now, the ratio of their ages will be 4:5. Find their present ages.

Solution :
Let the present age of Deklerk and Saniya be 3x and 4x years respectively.

After 5 years,

Deklerk's age = 3x + 5

Saniya's age = 4x + 5

According to the question

(3x + 5) / (4x + 5) = 4 /5

⇒ 5 (3x + 5) = 4 (4x + 5) [ Cross multiplication]

⇒ 15x + 25 = 16x + 20

⇒ 15x - 16x = 20 -25

⇒ -x = -5

⇒ x = 5

∴ Deklerk's present age = 3x = 3(5) = 15 years

and Saniya's age = 4x = 4(5) = 20 years.
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