How long did I walk ?
One day I went for a walk in the morning at x minutes past 5'0 clock, where x is a two digit number. When I returned. it was y minutes past 6'0 clock. and I noticed that (i) I walked exactly for x minutes and (ii) y was a 2 digit number obtained by reversing the digits of x. How many minutes did I walk?
- Pre Indian Regional Mathematics Olympiad - 2019
The answer is 42.
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1 solution
(ii) y was a 2 digit number obtained by reversing the digits of x
x = 10a + b < 60
y = 10b + a < 60
This means that both a and b are either 1,2 3,4 or 5
(i) I walked exactly for x minutes
60-x + y = x or 60 + y = 2x
Substituting for x and y from (ii) we have
60 + 10b+ a = 2*(10a +b) = 20a+2b or 19a -8b = 60
Just by substituting for some values for a and b intelligently we can easily arrive at the solution where a = 4 and b =2.
So I have left the house at 5:42 and have reached at 6:24 and have walked for 42 mins.