Question

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 what is the two digit number​

Answer 1

Step-by-step explanation:

Let the number be 10x+y

x+y = 5 …(1)

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

10x-x-10y+y= 27, or

9x-9y = 27, or

x-y = 3 …(2)

Add (1) and (2)

2x= 8, or

x = 4 and y = 1

So the number is 41 and its subsidiary is 14 and the difference between them is 27 and the sum of the digits is 5.

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.