Question

At what time between, four o’clock & five o’clock, are the hands $$2$$minutes space apart?

Answer 1

Hint: Clock concept: - The dial of the clock is circular in shape and was divided into $$60$$equal minute space.
$$60$$minute space traces an angle $${360}^0$$
$$1$$minute space traces an angle $${60}^0$$.


Complete step by step solution:
Minute spaces: The face or dial of watch is a circle whose circumference is divided into $$60$$equal parts, called minute spaces.
Hour hand & Minute hand: A clock has two hands, the smaller one is called the hour hand or shorthand, while the larger one is called minute hand or long hand.
In $$60$$equal minutes, the minute hand gains $$55$$minutes on the hour on the hour hand.
When the two hands are at right angles, they are $$15$$minutes spaces apart.
Angle traced by hour hand in $$12$$hours $$={360}^0$$.
Angle traced by minute hand in $$60$$min $$={360}^0$$.
Therefore,

At 4 o’clock the two hands are 20-minute spaces apart.

To be in 2 minute, they must be 2 minute spaces apart.
Minute hand will have to gain $$\left(20+2=22\right)$$minute spaces.
As we know that,
$$55$$minute spaces are gained in $$60$$minute.
$$22$$minute spaces are gained in $${\displaystyle \frac{60}{55}}\times 2$$minute$$=24$$minute.
Hence the hands will be $$2$$minute apart at $$24$$minute past.

Note: If the clock or watch indicates $$6$$hour $$10$$minute when the correct time is $$6$$, it is said that the clock is $$10$$minute too fast.
If it indicates $$6:40$$when the correct time is $$7$$, it is said to be $$20$$min slow.