Question

The sum of the digits of a two digit number is 12. The number obtained by interchanging the two digits exceeds the given number by 18. Find the number
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Answer 1

Given :

• The sum of the digits of a two digit number = 12
• The number obtained by interchanging the two digits exceeds the given number by 18.

To find :

• The number

Solution :

Let the two digit number = 10 x + y

where,

• x and y are the digits.

1st condition :-

• x + y = 12 -----(1)

2nd condition :-

⠀⠀⠀⇒ 10y + x = 10x + y + 18

⠀⠀⠀⇒ 10y + x - 10x - y = 18

⠀⠀⠀⇒ 9y - 9x = 18

⠀⠀⠀⇒ Take 9 common.

⠀⠀⠀⇒ 9(y - x) = 18

⠀⠀⠀⇒ y - x = 18/9

⠀⠀⠀⇒ y - x = 2

• - x + y = 2 ----(2)

Solve (1) and (2)

⠀⠀⠀⠀⠀⠀x + y = 12

⠀⠀⠀⠀⠀- x + y = 2

⠀⠀⠀⠀______________

⠀⠀⠀⠀⠀⠀⠀2y = 14

⠀⠀⠀⠀________________

⠀⠀⠀⇒ 2y = 14

⠀⠀⠀⇒ y = 14/2

⠀⠀⠀⇒ y = 7

The value of y = 7.

Substitute the value of y in (1)

⠀⠀⠀⇒ x + y = 12

⠀⠀⠀⇒ x + 7 = 12

⠀⠀⠀⇒ x = 12 - 7

⠀⠀⠀⇒ x = 5

The value of x = 5.

The two digit number = 10x + y

⠀⠀⠀⇒ 10 × 5 + 7

⠀⠀⠀⇒ 50 + 7

⠀⠀⠀⇒ 57

∴ The two digit number = 57.

Answer 2

Given,

• The sum of the digits of a two digit number is 12.
• The number obtained by interchanging the two digits exceeds the given number by 18.

To Find,

• The Number.

Solution,

Let's,

The First Digit = X

The Second Number = Y

Then,

The Number = 10 × X + Y

= 10X + Y

After Interchanging Digits,

The First Digit = Y

The Second Number = X

Then,

The Interchanged Number = 10 × Y + X

= 10Y + X

The Interchanged Number Exceed By 18 to the Real Number •••(Given)

10X + Y = 10Y + X + 18

10X – X = 10Y – Y + 18

9X = 9Y + 18

9X – 9Y = 18

9(X – Y) = 18

X – Y = 18/9

X – Y = 2

X + Y = 12

X – Y = 2

X – Y = 2

X = Y + 2

X + Y = 12

Y + 2 + Y = 12

2Y + 2 = 12

2Y = 12 – 2

2Y = 10

Y = 10/2

Y = 5

X = Y + 2

X = 5 + 2

X = 7

Required Answer,

The Interchanged Number = 10X + Y

= 10(7) + 5

= 70 + 5

= 75

So,

The Number = 57