## Problems on Ages

The questions in this topic are solved using Linear Equations:

For a quick revision of linear equations concepts, click this link:

Linear Equations

1. Use variables such as x, y to represent ages of the persons involved in such questions.

2. Set up linear equations for the information given in the questions.

The following examples will illustrate the method of solving problems in this topic:

1. Ram is 2 years older than his brother Shyam. In 5 years from now, the sum of the ages of the brothers will be 20. How old is each today?

Solution:

Let Shyam’s age be x, then

Ram’s age is x + 2 (Ram is 2 years older than Shyam, x)

In 5 years from now, each will grow by 5 years and therefore,

Ram’s age will be x + 2 + 5, i.e., x + 7and

Shyam’s age will be x + 5,

Now, set up the following linear equation for the information that their age will add to 20 in 5 years from now:

(x + 7) + (x + 5) = 20

2x + 12 = 20, 2x = 8, i.e. x = 4.

So, Shyam is 4 years old today and Ram, 6 years.

2. In 10 years from now, Mike will be twice as old as his younger brother Mac. How old will each be 10 years from now, if they are 54 years old together 10 yearsfrom now?

Solution:

Take Mac’s age today to be x, then

In 10 years from now, he will be x +10

In 10 years from now, Mike is 2 times as old as Mac, therefore

Age of Mike = 2 × (x + 10) = 2x +20

Together they are 54 years old 10 years from now, then

(x + 10) +2x + 20 = 54,

3x + 30 = 54, 3x = 24, x = 8

So, Mac is 8 years old today, therefore in 10 years he will be

8 + 10 = 18, and

Mike will be 2 × 18 = 36