Question

What fraction of a clockwise revolution does the hour hand of a clock turn through, when it goes from (a) 3 to 9 (b) 4 to 7 (c) 7 to 10 (d) 12 to 9 (e) 1 to 10 (f) 6 to 3.

Answer 1

Hint: For solving this question you should know about the segments of a clock. As we know that the total number of segments in the clock is 12 and every segment is covered at the end of each hour. We will use this concept to solve this question. We will use this concept to solve this question. We will count the total hours in every segment and then divide it by total segments of a clock and find the next point by the given fraction if there is given that.

Complete step by step answer:
According to our question we have to ask to find the fractions of a clockwise revolution the hour hand of a clock turns through when it goes from the given time.
So, as we know that the total number of segments in a clock is 12. And for counting the fractions of a clockwise segment we will use the total number of hours as 12. And then we calculate the difference between both the timings or find the difference of hours.
So, as we see,
(a) the situation from 3 to 9 on clock the difference is 6, so the fraction of clockwise revolution \[=\dfrac{6}{12}=\dfrac{1}{2}\]
(b) the situation from 4 to 7 on clock the difference is 6, so the fraction of clockwise revolution \[=\dfrac{3}{12}=\dfrac{1}{4}\]
(c) the situation from 7 to 10 on the clock, the difference is 3. So, the fraction of clockwise revolution \[=\dfrac{3}{12}=\dfrac{1}{4}\]
(d) the situation from 12 to 9 on the clock, the difference is 9. So, the fraction of clockwise revolution \[=\dfrac{9}{12}=\dfrac{3}{4}\]
(e) the situation from 1 to 10 on the clock the difference is 9. So, the fraction of clockwise revolution \[=\dfrac{9}{12}=\dfrac{3}{4}\]
(f) the situation from 6 to 3 on the clock, the difference is 3. So, the fraction of clockwise revolution \[=\dfrac{3}{12}=\dfrac{1}{4}\]
So, the fractions of these are \[\dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{4},\dfrac{3}{4},\dfrac{3}{4},\dfrac{1}{4}\] respectively.

Note: While solving this question you should be careful for the total segments of that given and always find the difference of that points or hours and it will be counted through a given point from where it will start. And if the starting point is not given then start that from 00:00 or 12:00 in both the conditions the answer will be the same.