Question

there is a number between 10 and 100. the number is 8 times the sum of its digits if 45 is subtracted from it, the result is the number formed by interchanging its digits. find the number.​

Answer 1

Answer:

The number is 72

Step-by-step explanation:

Let the digits of the number be xy.

The value of the number will be 10x+y.

10x+y = 8(x+y)

2x-7y = 0. --------------- eq 1

10x+7-45 = 10y+x

9x-9y = 45

x-y = 5. --------------- eq 2

Multiplying eq 2 by -2 , we get

-2x+2y = -10

Adding to eq 1

-5y = -10

y = 2

x - y = 5

x = 7

So the number is 72.

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Answer 2

Answer:

72

Step-by-step explanation:

suppose the number is: AB

According to the question

AX10+ B= 8(A+B)

=>10A+B = 8A+8B

=> 10A-8A=8B-B

=> 2A = 7B

Hence A=7, B=2

The number is 72,

Again 72 -45= 27

thus proved