Question

sum of the digits of a two digit number is 7 . After interchanging the digit new number formed is 45 more then the original number. find the number.

Answer 1

Answer:

16

Step-by-step explanation:

Given:-

Sum of the digits of a two digit number is 7 . After interchanging the digit new number formed is 45 more then the original number.

To Find:-

The original number

Solution:-

Let unit's digit be x

∴ ten's digit = 7-x

Original number = 10(7-x) + x

→ 70 - 10x + x

→ 70 - 9x

Number after interchanging its digits = 10x + 7 - x

→ 9x + 7

It is given that the number after interchanging its digits is 45 more than the original number. So, if we add 45 to the original number it will be equal to the number after interchanging its digits.

ACQ,

∴ 9x + 7 = 70 - 9x + 45

⟹ 9x + 9x = 70 + 45 - 7

⟹ 18x = 108

⟹ x = 108/18

⟹ x = 6

Original number = 70 - 9x

⟹ 70 - 9(6)

⟹ 70 - 54

⟹ 16

Answer 2

Answer:

Let the digits be x and y

so first equation =

$x + y = 7$

second equation

$10x + y + 45 = 10y + x \\ 10x + y - 10x - y = ( - 45) \\ 9x - 9y = ( - 45) \\ x - y = 5$

so

$x + y = 7 \\ x - y = 5 \\ - \: + \: \: \: \: \: \: - \: \: \\ \\ 2y = 2 \\ y = \frac{2}{2} = 1$

so one digit of the number is 1 and another is

x+y=7

x+1=7

x=7-1

x=6

So the number is 16