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InterviewSolution
| 1. |
At what time between 2 and 3 the acute anglebetween the hour hand and the minute hand will be50° |
| Answer» <p>to find 1 minute</p><p>as we know clock has a circle shape</p><p>and we know that angle of a circle=360 degree</p><p>we know that it completes a circle in 1 hour</p><p>1 hour=60 min</p><p>hence</p><p>60 min = 360 degree</p><p>1 min = 360 /60 = 6degree</p><p>Finding 1 hour</p><p>12 hours = 360º</p><p>1 hour = 360 ÷ 12 = 30degree</p><p>Defining y</p><p> the minute hand be pointing to y min</p><p>Finding the angle that the minute hand made:</p><p>1 min = 6degree</p><p>y min = 6y degree</p><p>Finding the angle that the hour hand made</p><p>The hour hand is between 2 and 3 o'clock</p><p>hour hand = (2 * 30) + (y/60 *30) = (60 + y/2)degree</p><p>Solve for y</p><p>The angle between the hour hand and minute hand is 50 degree</p><p>6y - (60 + y/2) = 50</p><p>6y - 60 - y/2 = 50</p><p>6y-y/2=50+60</p><p>taking lcm of L.H.S</p><p>11y/2 = 110</p><p>11y = 110*2</p><p>11y = 220</p><p>y=220/11</p><p>y=20</p><p> hence minute hand is at 20 position</p><p>time= 2:20</p> <p>thank you very much </p> | |