Question

The sum of the digits of a 2-digit number is 11. The number obtained by
interchanging the digits exceeds the original number by 27. Find the number.​

Answer 1

Answer:

,

Explanation:

the given two digit number is found to be 47.

let the number in ones place be x and the number in tens place be y

given that x+y=11

y=11-x

=10y+x

=10(11-x)+x

=110-10x+x

=110-9x

after inter changing,

= 10x+y

=10(x)+(11-x)=11+9x

11+9x=110-9x+27

9x+9x=110-11+27

18x=126

x=126/18=7

y=11-x=11-7=4

therefore the number is 47

Answer 2

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

• The sum of the digits of a 2-digit number is 11.

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

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

• What's the original number?

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

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

Therefore,

Number = 10x + y

Given that,

Sum of digits of a two digit number is 11.

x + y = 11........ eq(1)

• After reversing the digits will be = 10y + x

According to the question :-

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

Hence,

⟶ (10y + x) -(10x + y) = 27

⟶ 10y + x - 10x - y = 27

⟶ 9 y - 9x = 27

y - x = 3..........eq(2)

From eq(1), we get

⟶ x = 11 - y

Now, put x = y-11 in eq(2)

⟶ y - x = 3

⟶ y - 11 + y = 3

⟶ 2y = 3 + 11

⟶ 2y = 14

⟶ y = 7

Again, put the value of y in eq(1)

⟶ x = 11 - y

⟶ x = 11 - 7

⟶ x = 4

Therefore,

unit's place digit is = 7

Ten's place digit is = 4

____________________________________________________

Then, the original number will be

= 10x + y

= 10 × 4 + 7

= 47