Question

of the digits is 6. Find the number.
A certain number between 10 and 100 is 8 times the sum of its digits. If 45 is subtracted from it the digits will
be reversed. Find the number.
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Answer 1

Answer:

We have,

Suppose that the number=x and y

Then, the value of number is 10x+y

According to given question,

10x+y=8(x+y)

10x+y=8x+8y

10x−8x=8y−y

2x=7y

x=27y......(1)

Again, according to given question,

10x+y−45=10y+x

10x+y−x−10y−45=0

9x−9y−45=0

x−y−5=0......(2)

Put the value of x by equation (1) in equation (2) and we get,

27y−y−5=0

27y−2y−10=0

5y=10

y=2

Put the value of y in equation (1) and we get,

x−y−5=0

x−2−5=0

x=7

The number is

10x+y

=10×7+2

=72

Hence, this is the answer.