A number theory problem by Anik Mandal
A man who went out between 4 and 5 P.M and returned between 5 and 6 P.M. found that the hands of the clock had exactly changed spaces.When did he go out?
Note:Changed places indicates that the position of the hour hand had been taken by the minute hand and vice-versa.
If the answer is in the form of a/b minutes past 4 then find a+b.
The students who are able to solve the question must post a solution or give some hints regarding the question.
The answer is 3983.
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Let the minutes passed after 4 be x and Let the minutes passed after 5 be y we know that Hour Hand moves 1/2 degree per minute and Minute hand--6 degree per minute writing equations for each position, 120 + (1/2* x)= 6*y
12y - x= 240------------------------------------ Equ 1
150+ (1/2 * y) = 6*x 12x- y =300 -------------------------------------Equ 2
adding Equ 1 and 2 11x + 11y = 540 ----------------------------------equ 3
substracting Equ 1 and 2 13x - 13y = 60 -----------------------------------equ 4
on solving Equ 3 and 4 we get x= 3840/143 =a/b
a+b = 3840 + 143 = 3983