Question

The sum of the digits of a two-digit number is 7. When the digits are reversed, the number is increased by 27. Find the number

Answer 1

Answer:

4 and 3 I ink

Step-by-step explanation:

Answer 2

Question:-

• The sum of the digits of a two-digit number is 7 . When the digits are reversed , the number is increased by 27 . Find the number.

To Find:-

• Find the number.

Solution:-

Let the two numbers be a and b

Given ,

• a + b = 7 . . . . ( 1 )

According to the Question:-

Two digits are:-

• 10a + b . . . . ( 2 )

• a + 10b . . . . ( 3 )

Subtract equation ( 3 ) from ( 2 ):-

$\longrightarrow\sf \: 10a + b - ( 10b + a ) = 27$

$\longrightarrow\sf \: 10a + b - 10b - a = 27$

$\longrightarrow\sf \: 9a - 9b = 27$

$\longrightarrow\sf \: 9( a - b ) = 27$

$\longrightarrow\sf \: a - b = \cancel\dfrac { 27 } { 9 }$

$\longrightarrow\sf \: a - b = 3 . . . . ( 4 )$

Now ,

Add equation ( 1 ) and ( 4 ):-

$\longrightarrow\sf \: a + b + a - b = 7 + 3$

$\longrightarrow\sf \: 2a = 10$

$\longrightarrow\sf \: a = \cancel\dfrac { 10 } { 2 }$

$\longrightarrow\sf \: a = 5$

Substitute a in equation ( 1 ) to get ' b ' value:-

$\longrightarrow\sf \: a + b = 7$

$\longrightarrow\sf \: 5 + b = 7$

$\longrightarrow\sf \: b = 7 - 2$

$\longrightarrow\sf \: b = 2$

Hence ,

• The number is 25