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:

The required number is 72.

Step-by-step explanation:

Let the certain number between 10 and 100 be A.

Whose ones digit be y and tens digit be x.

Then, A = 10x + y

Let the reversed of the certain number be B.

Then, B = 10y + x

Given that:

• The number is 8 times the sum of its digits.

→ 8(x + y) = 10x + y

→ 8x + 8y = 10x + y

→ 10x - 8x = 8y - y

→ 2x = 7y

→ x = 7y/2 _____(i)

• If 45 be subtracted from it the digits will be reversed.

→ A - 45 = B

→ 10x + y - 45 = 10y + x

→ 10x + y - 45 - 10y - x = 0

→ 9x - 9y - 45 = 0

→ 9(x - y - 5) = 0

→ x - y - 5 = 0 _____(ii)

Substituting the value of x in eqⁿ (ii):

→ 7y/2 - y - 5 = 0

→ 7y/2 - 2y/2 - 10/2 = 0

→ (7y - 2y - 10)/2 = 0

→ 5y - 10 = 0

→ 5y = 10

→ y = 10/5

→ y = 2

Substituting the value of y in eqⁿ (i):

→ x = 7y/2

→ x = (7 × 2)/2

→ x = 7

∴ Certain number = A = 10x + y = 10 × 7 + 2 = 70 + 2 = 72

∴ Reversed number = B = 10y + x = 10 × 2 + 7 = 20 + 7 = 27

Answer 2

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 =.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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