Question

4. 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:

• Let the certain number between 10 and 100 = 10x + y

( here we let unit place is y and the tenth place is x )

• A. T. Q

10x + y = 8(x + y) ( A. T. Q the certain number is 8 times the sum of its digit so that's why 8(x+y) )

=> 10x + y = 8x + 8y

=> 10x - 8y = 8y - y

=> 2x = 7y eq. 1

• A.T.Q

If 45 is subtracted from that number then the number is reversed

So, 10x + y - 45 = 10y + x

=> 10x - x + y - 10y = 45

=> 9x - 9y = 45

=> 9( x - y) = 45

=> x - y = 45/9

=> x - y = 5

Multiply by 2 both the sides

=> 2x - 2y = 10 eq. 2

Now, subtracting equation 1 & 2

• 2x - 7y = 0

- 2x + 2y = - 10

=> - 5y = - 10

=> y = - 10/- 5

=> y = 2

Putting value of y in equation 1

2x = 7y

=> 2x = 7(2)

=> 2x = 14

=> x = 14/2

=> x = 7

So, the certain number is 10x + y = 10 (7) + 2 = 70 + 2 = 72 ans.