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# Five years ago, A's age was four times the age of B. Five years hence, A's age will be twice the age of B. Find their present ages.

The given question can be simplified using the linear equations in two variables.

## Answer: The present age of A is 25 years and that of B is 10 years.

Let's try to re-write the given information mathematically.

**Explanation:**

Let the present age of A be x years and the age of B be y years.

5 years ago | Present age | 5 years hence | |
---|---|---|---|

Age of A | (x - 5) | x | (x + 5) |

Age of B | (y - 5) | y | (y + 5) |

Given that five years ago, A's age was four times the age of B.

(x - 5) = 4(y - 5)

x - 5 = 4y - 20

x - 4y = 5 - 20

**x - 4y = -15** -----------------> equation (1)

Five years hence, A's age will be twice the age of B.

(x + 5) = 2(y + 5)

x + 5 = 2y + 10

x - 2y = 10 - 5

**x - 2y = 5 **-----------------> equation (2)

By solving equation (1) & (2) using the substitution method, we get,

x = -15 + 4y ** **-----------------> From equation (1)

Substituting value of x in equation (2): x - 2y = 5, we get,

[-15 + 4y] - 2y = 5

-15 + 4y - 2y= 5

2y = 5 + 15

2y = 20

y = 10

x = -15 + 4y = -15 + 4(10) = -15 + 40 = 25

The present age of A: x = 25 years

The present age of B: y = 10 years

### Thus, the present ages of A and B are 25 years and 10 years respectively.

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