Question

At what time between 6 and 7 will the hands be perpendicular "explanation"

Answer 1

Hi ,

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1 )The clock is divided into 60 equal

minute divisions .

2 ) One minute division = 360°/60° = 6 a part

3 ) In one minute , the hour moves 1°/2

4 ) In one minute , the minute hand gains

5½° more than hour hand .

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H = Initial position of hour hand

M = minutes

x = angle

Here ,

hands are perpendicular to each other

=> x = 90°

H = 6

If x = 90° then the hands of clock are

right angles twice in every hours .

i ) 30H - 11/2( M ) = x°

30× 6 - 11/2 ( M ) = 90°

180 - 90 = 11/2 ( M )

( 90 × 2 )/11 = M

180/11 = M

M = 16 4/11

=> 16 4/11 minutes after 6' O clock

ii ) 30( H ) - 11/2 ( M ) = - x°

30× 6 - 11/2 ( M ) = - 90°

180 + 90 = 11/2( M )

( 270 × 2 )/11 = M

540/11 = M

M = 49 1/11

Therefore ,

=> 49 1/11 minutes after 6' O clock

I hope this helps you.

: )