Question

A certain number between 10 and 100 is 8 times the sum of its digits and if 45 be subtracted from it , the digits will be reversed. Find the number ​

Answer 1

Answer:

72.

Explanation:

question

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

given

a. certain. no. between. 10.and.100

some. of. digit=8times.

subtract from. the. digit=45.

to.find.

find the number

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answer

answer =.72.

Step-by-step explanation:

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=7y/2

(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,

7y/2−y−5=0

7y−2y−10=0

•••••••••••••••••

2

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.

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