Question

sum of the digits of a two-digit number is 11. when we interchange the digits, it is found that the resulting new number is greater than the original number by 63 full stop find the two digit number.​

Answer 1

Answer

Two-digit number is 29  $\pink{\bigstar}$

Given

Sum of the digits of a two-digit number is 11. when we interchange the digits, it is found that the resulting new number is greater than the original number by 63

To Find

Two digit number

Solution

Let two-digit number be , " 10y + x "

A/c , " sum of the digits of a two-digit number is 11 "

$\pink{\bigstar}$  y + x = 11 ... (1)

A/c , " when we interchange the digits ,  the resulting new number is greater than the original number by 63 "

⇒ 10x + y = ( 10y + x ) + 63

⇒ 10x + y - 10y - x = 63

⇒ 9x - 9y = 63

⇒ 9 ( x - y ) = 63

$\pink{\bigstar}$  x - y = 7 ... (2)

Solve (1) + (2) ,

⇒ ( y + x ) + ( x - y ) = 11 + 7

⇒ 2x = 18

$\pink{\bigstar}$  x = 9

On sub. x value in (1) , we get ,

⇒ y + (9) = 11

⇒ y = 11 - 9

$\pink{\bigstar}$  y = 2

So , Two-digit number = 10y + x

⇒ 10(2) + 9

⇒ 20 + 9

$\pink{\bigstar}$  29

Answer 2

Answer:

Two digit number is 69.

Step-by-step explanation:

Assume that the one's digit number be y and ten's digit number be x.

Sum of the digits of a two-digit number is 11.

 → x + y = 11

→ x = 11 - y ..............(1)

When we interchange the digits the resulting new number is greater than the original number by 63.

Original Number: 10x + y and Reversed Number: 10y + x

→ 10y + y = (10x + y) + 63

→ 10y + x - 10x - y = 63

→ 9y - 9x = 63

→ 9 (y - x) = 63

→ y - x = 7

→ x = y - 7 .............(2)

On comparing (1) & (2) we get,

→ 11 - y = y - 7

→ 2y = 18

→ y = 9

Substitute value of y in (1)

→ x = 11 - 9

→ x = 2

Original Number: 10(2) + 9

= 29

Hence, the original number is 29.