Question

at what time between 1'o clock and 2'o clock the hands of the clock are opposite to each other​

Answer 1

Answer:

Opposite = 180°

We have formula

Angle = modulus of 30*h - 11/2 * m

where h is hours and m is minutes

180 = modulus of 30*1 - 11/2 m

180 = MOD 30-11/2m

We have two cases.

CASE 1

+180 = 30-11/2 m

150 = -11/2 m

m = 150 * 2/-11

= -300/11

= -27. 3/11. minutes

Since minutes can't be negative, case 1 is false.

CASE 2

-180 = 30-11/2 m

-210 = -11/2m

210 = 11/2 m

m = 210*2/11

= 420/11

= 38. 2/11. minutes past 1

Answer 2

The answer is

$38 \frac{2}{11} \: past \: 1'O clock$

GIVEN

Time = Between 1'O clock and 2'O clock

TO FIND

The time when hands of the clock are opposite to each other.

SOLUTION

We can simply solve the above problem as follows;

For the clock hands to make a straight line with each other, This means that the angle formed between them should be equal to 180°

The Hour hand will be at 1

And,

The minute hand should gain, 5+ 30 = 35 minutes

Spaces to hour hand.

Gains of Minute hand in 1 Hour = 55 minutes.

So, In 35 minutes,

=

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

Hence, The answer is

$38 \frac{2}{11} \: past \: 1'O clock$

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