Question

The difference between two whole numbers is 66 and the ratio of the two numbers is 2 : 5. Then the two
numbers are:

Answer 1

Given :

• Ratio of the two whole numbers = 2 : 5
• Difference between the two whole numbers = 66

To find :

• The two numbers

Solution :

Let the two whole numbers be 2x and 5x.

• First number = 2x
• Second number = 5x

$\red\bigstar\underline{\boldsymbol{According~to~the~question,}}$

$\longmapsto \tt{2x - 5x = 66} \\ \\ \quad \longmapsto \tt - 3x = 66 \\ \\ \longmapsto \tt - x = \dfrac{66}{3} \\ \\ \longmapsto \tt - x = 22 \\ \\ \longmapsto \tt x = - 22$

The value of x = - 22

The two numbers are :-

• First number = 2x = 2 × (-22) = - 44
• Second number = 5x = 5 × (-22) = -110

_______________________________

Let's verify :-

Substitute the value of x in 2x - 5x = 66

Taking Lhs,

$\longmapsto \tt 2x - 5x \\ \\ \longmapsto \tt 2 \times ( - 22) - 5 \times ( - 22) \\ \\ \longmapsto \tt - 44 + 110 \\ \\ \longmapsto \tt 66$

66 = 66

Lhs = Rhs

Hence, verified.