Question

The digit at ten s place of 2-digit number is 3 times of that in one s place. If the digit are reversed the new number will be 36 less than the original no . Find the number

Answer 1

The 2 digit number represented by XY is 10X+Y.

Your first restrictions is X=3Y. giving you only 3 options 31,62,93.

2nd restrictions is 10Y+X=10X+Y−3610Y+X=10X+Y−36

You can cross out 31 and need to test the other two:

26=62–36: yep39=93–36: no

There's your answer.

If you want a general answer then you need to solve the 2 equations:

10Y+X=10X+Y−3610Y+X=10X+Y−36

X=3YX=3Y

With limitations 0<X<10, 0<=Y<10 and X,Y are integers.

Replacing X with 3Y you get

10Y+3Y=30Y+Y−3610Y+3Y=30Y+Y−36

13Y=31Y−36

18Y=3618Y=36

Y=2Y=2

X=6