# Ten years later, A will be twice as old as B and five years ago, A was three times as old as B. What is the present age of B?

Hint: So, when we get problems with finding ages, we’ll translate the question into algebraic equations using the phrases and variables using the information given. Then, we’ll solve the equations using methods such as elimination with proper calculations and get the final answer.

Complete step by step answer:

Let A and B the two present ages

Ten years from now, A is twice as old as B

(A + 10) = 2(B+ 10)

So, by solving the Equation we get

A = 2B + 10 Equation --(1)

Five years ago, A was 3 times as old as B

(A - 5) = 3(B - 5)

So, by solving the Equation we get

A = 3B - 10 Equation --(2)

By equating the Equation (1) and Equation (2)

We’ll get,

2B + 10 = 3B - 10

$\Rightarrow$ B = 20

So, the present age of B is 20.

NOTE:

While dealing with these types of problems keep in mind these quick tips:-

1. If the age of the person is x years then,

2. Age after k years will be x + k

3. Age before k years will be x – k

4. The age k times would be kx