Question

A $12$ dial clock has its minute hand defective.Whenever it touches dial $12$, it immediately falls down to $6$ instead of running smoothly (the hour hand remains unaffected during that fall). It was set right at $12$ 'O' clock in the noon.

At the time half past three, the angle between hour and minute hands of the watch will be -

• A. ${75}^o$
• B. ${60}^o$
• C. ${90}^o$
• D. ${105}^o$

Answer 1

Answer: (A)

${75}^o$

The answer is option $A$

Speed of an hour hand $=\frac{360}{(12\times 60)}={0.5}^o/hr$

At $3$'O clock, the minute had would've fallen down to $6$ and the hour hand would be in $3$

In $30$ mins, the minute hand would again move to $12$ and fall down to $6$

The distance covered by the hour hand in this $30$ mins $=30\times 0.5={15}^o$

$\therefore$ The hour hand has moved ${15}^o$ from the number $3$ on the clock, while the minute hand is on number $6$ on the clock at $3:30$

$\therefore$ Angle between the hour and minute hand $=90-15={75}^o$