Question

The sum of the digits of a two digit number is 7. The numbers obtained by interchanging the digits exceeds the original number by 27. Find the number​

Answer 1

Let y = the original one's digit. Then 10x + y is the value of the original 2-digit number, and 10y + x is the value of the interchanged 2-digit interchanged number. The sum of the digits is 7: x + y = 7. Interchanged number exceeds original number by 27.

Answer 2

${ \huge{ \underline{ \underline{ \sf{ \green{GivEn : }}}}}}$

• Sum of digits = 7

• The numbers obtained by interchanging the digits exceeds the original number by 27.

${ \huge{ \underline{ \underline{ \sf{ \green{To \: find :}}}}}}$

• What's the number?

${ \huge{ \underline{ \underline{ \sf{ \green{SoluTion : }}}}}}$

let the ten's place digit and unit's place digit be x and y respectively.

Then

The number will be = 10x + y

After reversing,

Reversed number will be = 10y + x

Given that,

Sum of digits = 7

Therefore,

⟼ x + y = 7..........eq(1)

Again, it’s given that

The numbers obtained by interchanging the digits exceeds the original number by 27.

A.T.Q :-

⟼ 10y + x -(10x + y) = 27

⟼ 10y + x - 10x - y = 27

⟼ 9y - 9x = 27

⟼ y - x = 3........eq(2)

From eq(1), we get

⟼ x = 7 - y

Put x = 7 - y in eq(2)

⟼ y - x = 3

⟼ y -(7 - y) = 3

⟼ y - 7 + y = 3

⟼ 2y - 7 = 3

⟼ 2y = 3 + 7

⟼ y = 5

Substituting the value of y = 5 in eq(1), we get

⠀⠀⠀⠀⠀⟼ x = 7 - y

⠀⠀⠀⠀⠀⟼ x = 7 - 5

⠀⠀⠀⠀ ⟼⠀ x = 2

Hence,

The original number (10x + y)

= 2×10 + 5

= 25

Reversed number (10y + x)

= 10×5 + 2

= 52

Therefore, the number will be 25.

____________________________________________________

Verification :-

Given that,

⟼ Sum of digits = 7

⟼ 5 + 2 = 7

L.H.S = R.H.S

(verified)