Question

The sum of the digits of two-digits together with 7 is three times the digits in its tens place. If 8 be subtracted from the number the digits of the number inter change their position. Find the number.

Answer 1

Let number in tens place be 'a'
number in unit place be 'b'
a+b+7=3a
b=2a-7
10a+b=the number
in question it is given that if 8 is substracted from the number digits get interchanged. But practically there is no such number possible .
so let the number substracted is taken as 9 .change 8 to 9 and it works
After interchanging digits number become 'ba'
10a+b-9=10b+a
9a-9=9b
9a-9=9×(2a-7)
9a-9=18a-63
9a=63-9=54
a=54÷9=6
b=2×6-7
b=5
so the number is 'ab'=65
by putting this value in condition 65-9=56