Question

Show that the minute-hand of clock gains 5°30' on the hour-hand in one minute.

Answer 1

Angle made by hour-hand in one minute

= `(360°)/(12xx60)=(1/2)^circ`

Angle made by minute-hand in one minute

= `(360°)/60` = 6°

∴ gain of minute-hand on the hour-hand in one minute

= 6° − `((1)/2)^circ`

= `(6^circ xx 2)/1 − ((1)/2)^circ`

= `((12 - 1)/2)^circ`

= `((11)/2)^circ`               ...[∵ `((11)/2)^circ` is converted into mixed fraction]

= `5.5^circ` or `(5 1/2)^circ`         

= 5°30'