Question

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

Let the number between 10 and 100

= 10x + y

It is eight times the sum of its digits ⇒ 10x + y = 8(x + y) ⇒ 2x - 7y = 0 ....(1)

If 45 is subtracted from the number, the digits are reversed.

(10x + y) - 45 = (10y + x)

⇒ 9x - 9y = 45 ⇒ x - y = 5 .....(2)

By solving equations (1) and (2),

7y/2 - y = 5

5y/2 = 5

y = 2

So x = 7

we get x = 7 and y = 2.

Therefore, the original number is 72.

Answer 2

Answer:

72

Step-by-step explanation:

let the number be 10X+Y

given

10X+Y= 8(X+Y)

=> 2X-7Y= 0..............(1)

10X+Y-45 = 10Y+X

9X-9Y=45

X-Y= 5....................(2)

eqn(2) ×2

=> 2X-2Y= 10..............(3)

eqn(1) - eqn (3)

Y= 2

putting Y=2 in (2)

X-2= 5

=> X=7

therefore the number= 72