Basic FormulasRule 1Rule 2 |
Formula / Rule / Type 2 :-
Theorem:
Between x and (x +1) o 'clock the two hands12
are at right angle at (5x ± 15)x — minutes
11
Example:
what time between 4 and 5 o'clock will the hand of clock be at right angle?Detail Method:
At 4 o'clock, there are 20 min. spaces between hour and minute hands.To be at right angle, they should be 15 min spaces apart. So, there are two cases:
Case 1: When the minute hand is 15 min spaces behind the hour hand.
To be in this position, the min hand should have to gain 20 - 15 = 5 min spaces.
Now, we know that 55 min spaces are gained in 60 min
so 5 min spaces are gained in
60 5
— x 5 = 5 — min.
55 11
so they are at right angle at
5
5 — min past 4.
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Case 2: When the minute hand is 15 min spaces ahead of the hour hand.
To he in this position, the min hand should have to gain 20 + 15 = 35 min spaces.
No we know that 55 min spaces are gained in 60 min
so 35 min spaces will he gained in
60 2
— x 35 = 38 — min.
55 11
so they are at right angle at
2
38 — min past 4.
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Quicker Method:
Applying the above rule, we can say that they will be at right angle at12
(5 x 4 - 15) x — and
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12
(5 x 4 + 15) x — min past 4 or
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5
5 — min and
11
2
38 — min past 4.
11
Basic FormulasRule 1Rule 2 |