Question

the ratio of tens digit to the unit digit of a two digit number is 2 ratio 3 if 27 is added to the number the digits interchange their places find the number

Answer 1

Let +t+ = the tens digit
Let +u+ = the units digit
------------------------
(1) +t%2Fu+=+2%2F3+
(2) +10t+%2B+u+%2B+27+=+10u+%2B+t+
----------------------------
(2) +10t+-+t+%2B+27+=+10u+-+u+
(2) +9u+-+9t+=+27+
(2) +u+-+t+=+3+
----------------
(1) +t+=+%282%2F3%29%2Au+
Substitute (1) into (2)
(2) +u+-+%282%2F3%29%2Au+=+3+
(2) +%281%2F3%29%2Au+=+3+
(2) +u+=+9+
and
(2) +u+-+t+=+3+
(2) +t+=+u+-+3+
(2) +t+=+9+-+3+
(2) +t+=+6+
The original number is 69
check:
(2) +10t+%2B+u+%2B+27+=+10u+%2B+t+
(2) +10%2A6+%2B+9+%2B+27+=+10%2A9+%2B+6+
(2) +69+%2B+27+=+90+%2B+6+
(2) +96+=+96+
OK