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Time when minute hand and hour hand coincide
  • Difficulty Level : Basic
  • Last Updated : 24 Apr, 2018

Given time in hours, find the time in minute at which the minute hand and hour hand coincide in next one hour.

Examples :

Input : 3 
Output : (180/11) minutes

Input :7
Output : (420/11) minutes

Approach :
1. Take two variables for hour “h1 and h2” and then find the angle “theta” [theta = (30 * h1)] and then divide it by “11” to find the time in minute(m). We are dividing with 11, because the hands of a clock coincide 11s time in 12 hours and 22 times in 24 hours :

Formula : This can be calculated using the formula for time h1 to h2 means [11m / 2 – 30 (h1)]
this implies [ m = ((30 * h1) * 2) / 11 ] ]
[ m = (theta * 2) / 11 ]
where [theta = (30 * h1) ]



where A and B are hours i.e if given hour is (2, 3) then A = 2 and B = 3 .

C++

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// CPP code to find the minute at which 
// the minute hand and hour hand coincide
#include <bits/stdc++.h>
using namespace std;
  
// function to find the minute
void find_time(int h1)
  // finding the angle between minute 
  // hand and the first hour hand
  int theta = 30 * h1;
  cout << "(" << (theta * 2) << "/"
       << "11"
       << ")"
       << " minutes";
}
  
// Driver code
int main() {
  int h1 = 3;  
  find_time(h1);  
  return 0;
}

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JAVA

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// Java code to find the minute  
// at which the minute hand and 
// hour hand coincide
import java.io.*;
  
class GFG 
{
      
    // function to find the minute
    static void find_time(int h1)
    
      
    // finding the angle between 
    // minute hand and the first 
    // hour hand
    int theta = 30 * h1;
    System.out.println("(" + theta * 
                           2 + "/"
                   " 11 ) minutes");
    }
      
    //Driver Code
    public static void main (String[] args)
    {
        int h1 = 3
        find_time(h1);     
    }
}
  
// This code is contributed by 
// upendra singh bartwal

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Python3

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# Python3 code to find the 
# minute at which the minute
# hand and hour hand coincide
  
# Function to find the minute
def find_time(h1):
  
    # Finding the angle between 
    # minute hand and the first 
    # hour hand
    theta = 30 * h1 
    print("(", end = "")
    print((theta * 2),"/ 11) minutes")
  
# Driver code
h1 = 3
find_time(h1) 
  
# This code is contributed by
# Smitha Dinesh Semwal

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C#

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// C# code to find the minute 
// at which the minute hand 
// and hour hand coincide
using System;
  
class GFG 
{
      
    // function to find the minute
    static void find_time(int h1)
    
      
        // finding the angle between minute 
        // hand and the first hour hand
        int theta = 30 * h1;
        Console.WriteLine("(" + theta * 2 + 
                     "/" + " 11 )minutes");
    }
      
    //Driver Code
    public static void Main()
    {
        int h1 = 3; 
          
        find_time(h1); 
    }
}
  
// This code is contributed by vt_m.

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PHP

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<?php
// PHP code to find the minute 
// at which the minute hand and
// hour hand coincide
  
// function to find the minute
function find_time($h1)
    // finding the angle between 
    // minute hand and the first 
    // hour hand
    $theta = 30 * $h1;
    echo("(" . ($theta * 2) . 
           "/" . "11" . ")"
                 " minutes");
}
  
// Driver code
$h1 = 3; 
find_time($h1); 
  
// This code is contributed by Ajit.
?>

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Output :

(180/11) minutes

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