Question

the ratio of tens digit to the unit digit of a two digit number is 1 : 2 ,if 18 is added to the number the digits interchange their places .find the number

Answer 1

Ratio of the two digits = 1 : 2

Define the number:

Let the digit in the units place be x

And the digit in the tens place be y

⇒ The number is 10y + x

Form equation (1):

Ratio of the two digits = 1 : 2

⇒ x = 2y

Form equation (2):

18 is added to the number the digits interchange their places

⇒ 10y + x + 18 = 10x + y

⇒9y + 18 = 9x

⇒y + 2 = x

⇒ x = y + 2

Solve x and y:

x = 2y------------ (1)

x - y + 2 ------------- {2}

Equation (1) and (2) :

2y = y + 2

y = 2

x = 2y ------------ (1)

x = 2(2) = 4

Find the number:

Number = 10y + x = 10(2) + 4 = 24

Answer: The number is 24

Answer 2

Answer:

Ratio of the two digits = 1:2

Define the number:

Let the digit in the units place be x

And the digit in the tens place be y

→ The number is 10y + x

Form equation (1):

Ratio of the two digits = 1:2 ⇒ x = 2y

Form equation (2):

18 is added to the number the digits,

interchange their places

→ 10y + x + 18 = 10x + y

→ 9y + 18 = 9x

⇒y + 2 = x =>

⇒ x = y + 2

Solve x and y:

x = 2y--- (1)

X-y + 2 {2}

Equation (1) and (2):

2y = y + 2

y = 2

x = 2y (1)

x = 2(2) = 4

Find the number:

Number = 10y + x = 10(2) + 4 = 24

Answer: The number is 24

Explanation:

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