Question

n.
The sum of the digits of a two digit numbers is 7. If we add 45 to the number, the
digits are interchanged. Find the number.
NA
digit
i.​

Answer 1

Correct Question:-

The sum of the digits of a two digit number is 7. If we add 45 to the number, the digits are interchanged. Find the number.

Given:-

• The sum of the digits of a two digit number is 7.
• If we add 45 to the number, the digits are interchanged.

Solution:-

Let the unit place digit be " x "

Tenth place digit be " y "

Number = 10y + x

Here,

$\tt\implies \: y = 9 - x ......( 1 )$

$\tt\implies \: 45 + 10y + x = 10x + y$

$\tt\implies \: 10x - x = 10y - y + 45$

$\tt\implies \: 9x = 9y + 45$

$\tt\implies \: 9x - 9y = 45$

$\tt\implies \: 9( x - y ) = 45$

$\tt\implies \: x - y = 5 ........ ( 2 )$

Now,

Substitute y in equation 2

$\tt\implies \: x - ( 9 - x ) = 5$

$\tt\implies \: x - 9 + x = 5$

$\tt\implies \: 2x = 9 + 5$

$\tt\implies \: 2x = 14$

$\tt\implies \: x = 7$

Hence,

$\tt\implies \: y = 9 - x$

$\tt\implies \: y = 9 - 7$

$\tt\implies \: y = 2$

Now,

The number is

$\tt\implies \: 10y + x$

$\tt\implies \: 10(2) + 7$

$\tt\implies \: 20 + 7$

$\tt\implies \: 27$

Answer 2

$\orange{ \underline{ \large \sf \: Correct \: Question:-}}$

The sum of the digits of a two digit number is 7. If we add 45 to the number, the digits are interchanged. Find the number.

$\orange{ \underline{ \large \sf \: Given:-}}$

The sum of the digits of a two digit number is 7.

If we add 45 to the number, the digits are interchanged.

Solution:-

Let the unit place digit be " x "

Tenth place digit be " y "

Number = 10y + x

Here,

y = 9 - x ......( 1 )

45 + 10y + x = 10x + y

→ 10x - x = 10y - y + 45

→ 9x = 9y + 45

→ 9x - 9y = 45

→ 9( x - y ) = 45

→ x - y = 5 ........ ( 2 )

Now,

Substitute y in equation 2

x - ( 9 - x ) = 5

→ x - 9 + x = 5

→ 2x = 9 + 5

→ 2x = 14

→ x = 7 → x=7

Hence,

y = 9 - x

→ y = 9 - 7

→ y = 2⟹y=2

Now,

The number is

10y + x

→ 10( 2 ) + 7

→ 20 + 7

→ 27

Hope it's helpful