Question

# Choose the most appropriate option. A clock was set correct at $$12$$O' clock. It loses $$10$$ minutes per hour. What will be the angle between the hour and minute hands of the clock after one hour?

A
900
B
850
C
750
D
1050.

Solution

## The correct option is C $$85^0$$The clock loses $$10$$ minutes per hour.  Here, the clock shows only $$50$$ minutes for $$60$$ minutes ( in $$1$$ hour )The clock show the time $$12:50$$, after $$1$$ hour.We can find the angle between hour hand and minutes at $$H$$ hours $$M$$ minutes $$=30H-\dfrac{11}{2}M$$The angle between the two hands of the clock after $$1$$ hour $$=30\times 12-\dfrac{11}{2}\times 50$$                                                                                                    $$=360^o-11\times 12$$                                                                                                    $$=360^o-275^o$$                                                                                                    $$=85^o$$Logical Reasoning

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