Question

At what time between 4 and 5 o'clock will the hands of clock be at right angle?

Answer 1

At 4 o'clock there are 20 minutes spaces between hour and minute hands To be at right angle they should be 15 minutes spaces apart

So there are two cases :

Case I : When minute hand is 15 minute spaces behind the hour hand

To be in this position the minute hand should have to gain 20 - 15 = 5 minute spaces

Now we know that 55 minute spaces are gained in 60 minute

$\therefore$ 5 minutes spaces are gained in

$\frac{60}{55}\times 5=5\frac{5}{11}min$

Hence they are at right angle at $5\frac{5}{11}min$ past 4

Case II : When minute hand is 15 min spaces ahead of hour hand

To be in this position the minute hand should have to gain 20 + 15 = 35 minute spaces

Now we know that 55 minute spaces are gained in 60 minute

$\therefore$ 35 minute spaces will be gained in

$\frac{60}{55}\times 35=38\frac{2}{11}$ minute

Hence they are at right angle at $38\frac{2}{11}$ min past 4