Question

How many times between 6: 00 am and 6: 00 pm, do the hands of the clock make a straight line.
A. 9
B. 10
C. 11
D. 12

Answer 1

Hint: In this question using the diagram of a clock , find pairs of numbers which are parallel to each other and form a straight line with a small and large needle, use this information to approach the solution to the question.

Complete step-by-step answer:
To find the numbers of straight lines formed between 6: 00 am and 6: 00 pm let’s draw a diagram of clock

As we can see in the above diagram we have 2 needles in a clock larger needle represents the minutes and smaller represents the hour in clock.
As we know that there is a difference of 24 hours between 6:00 am to 6:00 pm.
Let’s see how many numbers are parallel to each other in the above diagram between 6: 00 am to 6: 00 pm
So after observing the above diagram as we can see that number 12 and 6 are parallel to each other where larger needle is at 12 and smaller needle is at 6 and here when a larger needle is at 12 and smaller needle at 6 it makes a straight lines similar happens when needles interchange their positions
So by the above statement since the 12 and 6 are parallel to each other so we can say that the numbers which are parallel to each other forms a straight lines
Since the larger needle and smaller needle will be positioned at every number between 6: 00 am to 6: 00 pm so the numbers parallel to each other will form 2 straight lines first line when larger needle is at first number and smaller needle at smaller number and the second straight line when needles interchange their positions
So the sets of numbers parallel between 6: 00 am to 6: 00 pm are (1, 7), (2, 8), (3, 9), (4, 10), (5, 11), (6, 12), (7, 1), (8, 2), (9, 3), (10, 4) and (11, 5)
So here each set makes a straight line
Since we have total 11 numbers of set of numbers parallel to each other between 6: 00 am to 6: 00 pm
So 11 are the total numbers of straight lines formed between 6: 00 am to 6: 00 pm.
Hence option C is the correct option.

Note: In the above solution the question was based on the clock system so let’s discuss the clock and why it is used. So the clock is an instrument which is used to represent the time with the help of pairs of needles which are named as minute hand and hour hand here the minute hand represents the minute which has the largest needle in clock then the smaller needle is represented by hour hand which shows hour in clock.