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 what angle are the hands of a clock inclined at $30$ minutes past $6$ ?

• A. $7{\frac{1}{2}}^{\circ }$
• B. $11{\frac{1}{2}}^{\circ }$
• C. ${15}^{\circ }$
• D. ${23}^{\circ }$

Answer 1

Answer: (C)

${15}^{\circ }$

The answer is option $C$

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

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

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 $=30\times 0.5={15}^o$

$\therefore$ Angle between minute and hour hand $={15}^o$