Question

15 years hence, A will be twice as old as B, but five years ago A was
4 times as old as B. Find the difference of their present ages. ​

Answer 1

Step-by-step explanation:

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Answer 2

Given - Age comparison 15 years ago and five years ago

Find - Difference of present ages

Solution - The difference in present ages is 30 years.

Let the age of A be x and the age of b be y years old. Now, 15 years later, their ages will be related as follows.

x + 15 = 2(y + 15)

Solving this we get -

x + 15 = 2y + 30

x - 2y = 15

Let this be equation 1.

Now, 5 years ago, their ages were as follows.

x - 5 = 4(y - 5)

x - 5 = 4y - 20

x - 4y = - 15

Let this be equation 2.

Solving the equation 1 and 2 for the value of y.

x - 2y = 15

x - 4y = - 15

On adding the two equations, we get, 2y = 30

y = 15

Finding the age of A-

x - 2(15) = 15

x - 30 = 15

x = 15 + 30

x = 45

So, the age of A is 45 years and the age of B is 15 years.

The difference between the present age = 45 - 15

Difference between the present age = 30 years.

Difference between their present ages is 30 years.