The sum of the digits of a certain two digit number is 11. reversing its digits decreases the number by 27 what is the number

74

Step-by-step explanation:

7+4=11

74-47=27

Let the digits of number be x and y

so,

number = 10y + x

given sum of digits = 11

so,

x + y = 11 ...(1)

also,

Reversing its digits decreases the number by 27

so,

reversed number = 10x + y

according to the question,

10x + y - (10y + x) = 27

10x + y - 10y - x = 27

9x - 9y = 27

9(x - y) = 27

x - y = 3. ...(2)

x + y + x - y = 11 + 3

2x = 14

x = 14/2

x = 7

putting the value of x on (2)

x - y = 3

7 - y = 3

-y = 3 - 7

- y = -4

y = 4

x = 7

so,

number = 10y + x

= 10(4) + 7

= 40 + 7

= 47

hope it helps !

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