At What Time Between 530 And 6 Will The Hands Of The Clock Be Inclined At 90°?

Sol:

At 5 o’clock, the hands are 25 min. Spaces apart.

To be at right angles between 5.30 and 6, the minute hand has to gain (25+15)=40 min spaces.

55 min. Spaces are gained in 60 min.

40 min spaces are gained in = $$\Rightarrow \frac{60 * 40}{55}$$ $$\Rightarrow 43\frac{7}{11}$$

Therefore, at the time $$43\frac{7}{11}$$min past 5, the hands of the clock are inclined at 90°.

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