Question

Sum of the digits of a two-digit number
is 5. When we interchange the digits, it is
found that the resulting new number is
less than the original number by 27.
What is the two-digit number?
​

Answer 1

Step-by-step explanation:

Two digit number = 10x + y

x + y = 5 -----(1)

digits are interchanged , so resulting number = 10y + x

10x + y - (10y + x) = 27

9x - 9y = 27

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

Solving both equation simultaneously, we get

x = 4 , y = 1

So, Original no = 10x + y = 10*4 + 1 = 41

Answer 2

Given:-

• Sum of the digit of a two digit number is 5.
• When we interchange the digit it is found that the resulting new number is less than the original number by 27.

To find:-

• Find the two digit number..?

Solutions:-

• Let the digits at ten's place be x.
• Let the digits at unit's place by y.

Number => 10x + y

Sum of the digit of a two digit number is 5.

=> x + y = 5

=> x + 5 - y ..........(i).

When we interchange the digit it is found that the resulting new number is less than the original number by 27.

• Reversed number = 10y + x
• Reversed number = original number - 26

=> 10y + x = 10x + y - 27

=> 27 = 10x + y - 10y - x

=> 27 = 9x - 9y

=> 27 = 9(x - y)

=> 27/9 = x - y

=> 3 = x - y ...........(ii).

Putting the value of x from Eq (i). in Eq (ii).

=> 3 = x - y

=> 3 = 5 - y - y

=> 3 = 5 -2y

=> 3 - 5 = -2y

=> -2 = -2y

=> y = -2/-2

=> y = 1

Putting the value of y in Eq (i).

=> x + 1 = 5

=> x = 5 - 1

=> x = 4

So, Number => 10x + y

=> 10(4) + 1

=> 40 + 1

=> 41

Hence, the number formed is 4.