4. A certain number between 10 and 100 is 8 times the sum of its digits, and if 45 be subtracted from.......
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Step-by-step explanation:
let us assume the digits to be x and y.
Hence, the original number will be:- 10x+y
And the reversed number will be :- 10y+x
Here according to the equation:-10x+y-45=10y+x
solving the above equation gives us:-
9x-9y=45
x-y=5 ....(1)
it was also given that:-
8(x+y)=10x+y
8x+8y=10x+y
0=2x-7y
from equation 1:-
2x-7y=0
2(y+5)-7y=0
2y+10-7y=0
5y=10
y=2
substituting in equation 1:-
x-y=5
x-2=5
x=7
so the original number is 72
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