Question

4. The sum of the digits of a two digit number is 12. The number obtained by interchanging the two digits exceeds
the given number by 18. Find the number. (2M

Answer 1

Answer:

The original number is 57

Step-by-step explanation:

Let us consider the digits of the two digit number be x and y

Therefore , the number is

$10x + y$

Given in the question :

The sum of the digits is 12

$x + y = 12 \\ \implies x = 12 - y$

Again given , the number obtained by interchanging exceeds the given number by 18

$10y + x = 10x + y + 18 \\ \implies10y - y = 10x - x + 18 \\ \implies9y = 9x + 18 \\ \implies y = x + 2 \\ \implies y = 12 - y + 2 \\ \implies y + y = 14 \\ \implies2y = 14 \\ \implies y = 7$

And since

$x = 12 - y$

so putting the value of y we have

$x = 12 - 7 \\ \implies x = 5$

Therefore, the original number is

$10 \times 5 + 7 \\ = 50 + 7 \\ = 57$

Answer 2

hey mate here is your answer,

Step-by-step explanation:

let the digit in unit place is = x

and the digit in tens place is = 12 - x

so, the number formed is = (12-x)10 + x

= 120 - 10x + x

= 120 - 9x

interchanging the digits ,

the digit in unit place is = 12 - x

the digit in tens place is = x

so, the new number formed is = (x)10 + 12 - x

= 10x + 12 - x

= 9x + 12

A/C to the condition 120 - 9x + 18 = 9x + 12

or, 138 - 9x = 9x + 12

or, - 9x - 9x = 12 - 138

or, - 18x = - 126

or, 18x = 126

or, x = 126/18

= 7

so, the number is is = 120 - 9x

= 120 - 63

= 57

plz, mark me as brainliest