# Ajay is younger than Vijay by 3 years. The sum of their ages is 25 years, what is the age of Ajay - Algebra

Sum

Ajay is younger than Vijay by 3 years. The sum of their ages is 25 years, what is the age of Ajay

#### Solution

Let the ages of Ajay and Vijay be x years and y years respectively.

According to the first condition,

Ajay is younger than Vijay by 3 years.

∴ y – x = 3

i.e., – x + y = 3   .....(i)

According to the second condition,

Sum of their ages is 25.

∴ x + y = 25   .....(ii)

Subtracting equation (i) from (ii), we get

x + y = 25
− x + y = 3
+    −      −
2x      = 22

∴ x = 22/2 = 11

∴ Ajay’s age is 11 years.

Alternate Method:

Let the age of Ajay be x years.

Ajay is younger than Vijay by 3 years.

∴ Vijay’s age = x + 3

According to the given condition,

Sum of their ages is 25.

∴ x + x + 3 = 25

∴ 2x + 3 = 25

∴ 2x = 22

∴ x = 22/2 = 11

∴ Ajay’s age is 11 years.

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Substitution Method
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