Question

Sum of the digits of a two digit number is 9. The number obtained by interchanging the digits exceeds the given number by 27. Find the given number. *

Answer 1

Given :-

Sum of the digits of a two digit number = 9

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

Required to find :-

• The original number ?

Solution :-

Let the unit's digit be x

Ten's digit be y

No. formed = 10 ( y ) + 1 ( x )

=> 10y + 1x

On reversing the digits ;

The unit digit = y

Ten's digit = x

No. formed = 10 ( x ) + 1 ( y )

=> 10x + y

Since,

The sum of the digits of two digit number is 9

y + x = 9

y = 9 - x $\tt{\bf{ Equation - 1 }}$

Consider this as equation 1

It is mentioned that ;

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

So,

According to problem ;

10y + x = 10x + y + 27

10y + x - 10x - y = 27

- 9x + 9y = 27

Substitute the value of y from equation 1

- 9x + 9 ( 9 - x ) = 27

- 9x + 81 - 9x = 27

- 18x = 27 - 81

- 18x = - 54

- ( minus ) get's cancelled on both sides

18x = 54

x = 54/18

x = 3

Now,

Substitute the value of x in equation 1

y + x = 9

y + 3 = 9

y = 9 - 3

y = 6

Hence,

• Value of x = 3

• Value of y = 6

So,

The original number can be 36 or 63

Now,

Let's find which number is the original number .

So,

According to the condition ;

The number obtained by interchanging the digits exceeds the given number by 27

This implies ;

Let's assume that 63 is the original number

According to condition ;

63 = 36-27

63 = 9

LHS ≠ RHS

Our assumption is wrong .

Similarly,

Let's assume that 36 is the original number

According to condition ;

36 = 63 - 27

36 = 36

LHS = RHS

Our assumption is correct

Therefore,

36 is the original number !!

Answer 2

Answer:

The number is 36

Step-by-step explanation:

Given:

• Sum of the digits of a two digit number = 9

• The number obtained by interchanging the digits exceeds the

given number by 27

To find :

• The given number

Solution:

Let,

Tens digit = x

Units digit = y

So,

➨ x + y = 9

➨ x = 9 - y --------(1)

Also

➨ 10x + y + 27 = 10y + x

➨ 9x - 9y = -27

➨ x - y = -3

Using (1) in above equation

➨ 9 - y - y = -3

➨ -2y = -12

➨ y = 6

Thus,

➨ x = 9 - 6

➨ x = 3

Therefore,

Original Number = 30 + 6

➨ 36

The number is 36