Question

The sum of digits of a two digit number is 11. If we interchange the digits then the new number formed is is 45 less than the original number. Find the original number.​

Answer 1

Answer:

• The original number is 38.

Step-by-step explanation:

Given that:

• The sum of digits of a two digit number is 11.
• If we interchange the digits, then the new number formed is 45 less than the original number.

To Find:

• The original number.

Let us assume:

• The digit at the ones place be x.

Then,

• The digit at the tens place will be 11 - x.

The original number:

$\sf{\longmapsto10(11-x)+1(x)}$

Opening the brackets,

$\sf{\longmapsto110-10x+x}$

Solving further,

$\sf{\longmapsto110-9x}$

Interchanging the digits:

$\sf{\longmapsto10(x)+1(11-x)}$

Opening the brackets,

$\sf{\longmapsto10x+11-x}$

Solving further,

$\sf{\longmapsto9x+11}$

According to the question:

$\sf{\longmapsto(110-9x)-(9x+11)=45}$

Opening the brackets,

$\sf{\longmapsto110-9x-9x-11=45}$

Solving further,

$\sf{\longmapsto99-18x=45}$

Transposing 99 from LHS to RHS and changing its sign,

$\sf{\longmapsto-18x=45-99}$

Subtracting RHS,

$\sf{\longmapsto-18x=-54}$

$\sf{\longmapsto18x=54}$

Transposing 18 from LHS to RHS and changing its sign,

$\sf{\longmapsto x=\dfrac{54}{18}}$

Dividing,

$\sf{\longmapsto x=3}$

Hence,

• x = 3

Therefore,

• Digit at the ones place = x = 3
• Digit at the tens place = 11 - x = 11 - 3 = 8
• The number is 38.

Answer 2

Answer:

The original number is 38.

Step-by-step explanation:

Given that:

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

If we interchange the digits, the new number formed is 45 less than the original.

To Find:

The original number.

Let us assume:

The digit in the one's place is x.

Then,

The digit at the tens place will be 11 - x.

The original number:

Opening the brackets,

Solving further,

Interchanging the digits:

Opening the brackets,

Solving further,

According to the question:

Opening the brackets,

Solving further,

Transposing 99 from LHS to RHS and changing its sign,

Subtracting RHS,

Transposing 18 from LHS to RHS and changing its sign,

Dividing,

Hence,

x = 3

Therefore,

Digit at the ones place = x = 3

Digit at the tens place = 11 - x = 11 - 3 = 8

The number is 38.Answer:

The original number is 38.

Step-by-step explanation:

Given that:

The sum of digits of a two digit number is 11.

If we interchange the digits, the new number formed is 45 less than the original.

To Find:

The original number.

Let us assume:

The digit at the ones place be x.

Then,

The digit at the tens place will be 11 - x.

The original number:

Opening the brackets,

Solving further,

Interchanging the digits:

Opening the brackets,

Solving further,

According to the question:

Opening the brackets,

Solving further,

Transposing 99 from LHS to RHS and changing its sign,

Subtracting RHS,

Transposing 18 from LHS to RHS and changing its sign,

Dividing,

Hence,

x = 3

Therefore,

Digit at the ones place = x = 3

Digit at the tens place = 11 - x = 11 - 3 = 8

The number is 38.