CLOCK AND CALENDAR
Note: Question numbers are numbers from the actual exam in the respective years mentioned below
- Between 6 PM and 7 PM the minute hand of a clock will be ahead of the hour hand by 3 minutes at(2015)
(A) 6:15 PM
(B) 6:18 PM
(C) 6:36 PM
(D) 6:48 PM
Answer-C
Between 6 PM and 7 PM, the hour hand and the minute hand coincide at 6 hr and ‘m’ minutes.
m= (30*2)/11 hours = (30*60*2)/11 minutes = 32 8/11
Hence, the hour hand and minute hand coincide at 6 hr 32 8/11 mins.
After 3 minutes, i.e. at 6 : 36 PM the minute hand of a clock will be ahead of the hour hand by 3 minutes.
- If second and fourth Saturdays and all Sundays are taken as only holidays for an office, what would be the minimum number of possible working days of any month of any year?(2017)
(A) 23
(B) 22
(C) 21
(D) 20
Answer-B
In a month with 28 days (non-leap year February), there are 4 Saturdays (2nd, 9th, 16th, and 23rd) and 4 Sundays. So, there are 28 -6 = 22 possible working days.
- A watch loses 2 minutes in every 24 hours while another watch gains 2 minutes in every 24 hours. At a particular instant, the two watches showed an identical time. Which of the following statements is correct if 24-hour clock is followed?(2017)
(A) The two watches show the identical time again on completion of 30 days.
(B) The two watches show the identical time again on completion of 90 days.
(C) The two watches show the identical time again on completion of 120 days.
(D) None of the above statements is correct.
Answer-D
Let's call the first watch that loses 2 minutes per day "Watch A" and the second watch that gains 2 minutes per day "Watch B".
Since Watch A loses 2 minutes per day and Watch B gains 2 minutes per day, the difference in time between the two watches will increase by 4 minutes per day (2 minutes lost by Watch A plus 2 minutes gained by Watch B).
To find out when the two watches will show the identical time again, we need to determine when the net time difference between them becomes a multiple of 24 hours or 1440 minutes (since there are 24 hours in a day and 60 minutes in an hour).
The time difference of 4 minutes per day means it will take 1440 / 4 = 360 days for the watches to align again and show the same time.
So,(d) None of the above statements is correct.
- A clock strikes once at 1 o'clock, twice at 2 o'clock and thrice at 3 o'clock, and so on. If it takes 12 seconds to strike at 5 o'clock, what is the time taken by it to strike at 10 o'clock?(2017)
(A) 20 seconds
(B) 24 seconds
(C) 28 seconds
(D) 30 seconds
Answer-B
Takes 12 seconds to strike at 5 o'clock
So at 10 o’clock ,it takes 2*12 seconds i.e, 24 seconds
- A wall clock moves 10 minutes fast every 24 hours. The clock was set right to show the correct time at 8:00 a.m. on Monday. When the clock shows the time 6:00 p.m. on Wednesday, what is the correct time?(2019)
(A) 5:36 p.m.
(B) 5:30 p.m.
(C) 5:24 p.m.
(D) 5:18 p.m.
Answer-A
To solve this problem, let's break it down step by step:
The clock moves 10 minutes fast every 24 hours. This means that for every 24-hour period, the clock gains 10 minutes.
The clock was set right to show the correct time at 8:00 a.m. on Monday. We need to determine the correct time when the clock shows 6:00 p.m. on Wednesday, which is a span of 2 days and 10 hours (Monday, Tuesday, and Wednesday until 6:00 p.m.).
In 2 days, the clock gains 2 * 10 = 20 minutes due to being 10 minutes fast each day.
In 10 hours, the clock gains an additional 10 * (10/24) = 4.1667 minutes (since it gains 10 minutes every 24 hours).
Therefore, the total gain of the clock from 8:00 a.m. on Monday to 6:00 p.m. on Wednesday is 20 minutes + 4.1667 minutes = 24.1667 minutes.
To determine the correct time, we subtract this gain from the time shown on the clock at 6:00 p.m. on Wednesday:
6:00 p.m. - 24.1667 minutes = 5:35.8333 p.m.
Since the minutes should be in increments of 6 (due to the clock's accuracy), we can round 5:35.8333 to the nearest multiple of 6, which is 5:36 p.m.
Therefore, the correct time is 5:36 p.m., which corresponds to option (a).
- Which year has the same calendar as that of 2009 ?(2019)
(A) 2018
(B) 2017
(C) 2016
(D) 2015
Answer-D
A calendar year is repeated every 7 odd days. Now, 7 odd days will come in 6 years (5 non leap years and 1 leap year). Hence, 2015 is the correct answer.
- Mr X has three children. The birthday of the first child falls on the 5th Monday of April, that of the second one falls on the 5th Thursday of November. On which day is the birthday of his third child, which falls on 20th December?
(A) Monday
(B) Thursday
(C) Saturday
(D) Sunday
Answer-B
Given:
The first child's birthday falls on the 5th Monday of April.
The second child's birthday falls on the 5th Thursday of November.
To find the day for the third child's birthday in December:
We examine the possible dates for the 5th Monday of April. It can either be on April 29th or April 30th.
If the 5th Monday of April is on April 29th:
Counting the days from April 30th to November 1st, we have 186 days. Dividing this by 7, we get 26 weeks and 4 odd days. Thus, November 1st is on a Friday.
However, November 29th and 30th are Friday and Saturday, respectively, which means it cannot be the 5th Thursday.
If the 5th Monday of April is on April 30th:
Counting the days from May 1st to November 1st, we have 185 days. Dividing this by 7, we get 26 weeks and 3 odd days. Thus, November 1st is on a Thursday.
In this case, November 29th is the 5th Thursday.
Therefore, the second child's birthday is on November 29th, which is a Thursday.
Looking at December, we have the following Thursdays: 6th, 13th, 20th, and 27th.
The third child's birthday falls on December 20th, which is a Thursday.
Hence, the correct answer is (b) Thursday.
- If in a particular year 12th January is a Sunday, then which one of the following is correct?(2020)
(A) 15th July is a Sunday if the year is a leap year.
(B) 15th July is a Sunday if the year is not a leap year.
(C) 12th July is a Sunday if the year is a leap year.
(D) 12th July is not a Sunday if the year is a leap year.
Answer-C
Considering the given year in which 12th January is a Sunday, we can determine the day of the week for 12th July based on the leap year rule and the knowledge that there are 365 days in a non-leap year and 366 days in a leap year.
Since we know that a leap year is divisible by 4 and not divisible by 100, or it is divisible by 400, we can determine the day of the week for 12th July as follows:
In a non-leap year, the days of the week advance by 1 day. If 12th January is a Sunday, then 12th July will be a Thursday.
In a leap year, the days of the week advance by 2 days. If 12th January is a Sunday, then 12th July will be a Sunday.
Considering the options:
(a) 15th July is a Sunday if the year is a leap year.
This statement is not directly related to the given information about 12th January. Therefore, option (a) is not correct.
(b) 15th July is a Sunday if the year is not a leap year.
This statement contradicts the previous analysis that in a non-leap year, 12th July is a Thursday. Therefore, option (b) is not correct.
(c) 12th July is a Sunday if the year is a leap year.
This statement aligns with our analysis that in a leap year, 12th July will indeed be a Sunday. Therefore, option (c) is correct.
(d) 12th July is not a Sunday if the year is a leap year.
This statement contradicts the previous analysis that in a leap year, 12th July is a Sunday. Therefore, option (d) is not correct.
Based on the analysis, the correct statement is (c) 12th July is a Sunday if the year is a leap year.
- Consider two Statements and a Question:
Statement-1: The last day of the month is a Wednesday.
Statement-2: The third Saturday of the month was the seventeenth day.
Question: What day is the fourteenth of the given month?
Which one of the following is correct in respect of the Statements and the Question?(2021)
(A) Statement-1 alone is sufficient to answer the Question
(B) Statement-2 alone is sufficient to answer the Question
(C) Both Statement-1 and Statement-2 are required to answer the Question
(D) Neither Statement-1 alone nor Statement-2 alone is sufficient to answer the Question
Answer-B
Statement-1: The last day of the month is a Wednesday.
This statement alone does not provide enough information about the day of the week for the fourteenth day of the month. The month could have 28, 29, 30, or 31 days, and we cannot determine the day for the fourteenth day based solely on the information given in Statement-1.
Statement-2: The third Saturday of the month was the seventeenth day.
This statement provides specific information about the seventeenth day of the month, which is the third Saturday. Knowing that the seventeenth day is a Saturday, we can deduce the day of the week for the fourteenth day by subtracting three days (3 odd days) from Saturday. Therefore, the fourteenth day will be a Wednesday.
By considering Statement-2 alone, we can answer the question and determine that the fourteenth day of the given month is a Wednesday.
Hence, option (b) Statement-2 alone is sufficient to answer the question.
- Which day is 10th October, 2027?(2021)
(A) Sunday
(B) Monday
(C) Tuesday
(D) Saturday
Answer-A
We all know that 10th October 2021 is a Sunday.How?
Because it's the day of UPSC CSE, 2021 Preliminary exam.
So, 10th October 2022 will be Sunday + 1, i.e. Monday
10th October 2023 will be Monday + 1, i.e. Tuesday.
Since 2024 is a leap year we should add 2
10th October 2024 will be Tuesday + 2, i.e. Thursday.
10th October 2025 will be Thursday + 1, i.e. Friday
10th October 2026 will be Friday + 1, i.e. Saturday
10th October 2027 will be Saturday + 1, i.e. Sunday.
- At which one of the following times, do the hour hand and the minute hand of the clock make an angle of 180° with each other?(2021)
(A) At 7:00 hours
(B) Between 7:00 hours and 7:05 hours
(C) At 7:05 hours
(D) Between 7:05 hours and 7:10 hours
Answer-D
To determine the time at which the hour hand and the minute hand of a clock make an angle of 180 degrees, we need to consider the relative positions of the hour and minute hands.
The minute hand completes a full rotation every 60 minutes, covering 360 degrees. This means that each minute, the minute hand moves by 360/60 = 6 degrees.
The hour hand completes a full rotation every 12 hours, covering 360 degrees. This means that each hour, the hour hand moves by 360/12 = 30 degrees. However, the hour hand also moves slightly between each hour, depending on the minutes elapsed within that hour.
Now let's analyze the given options:
(a) At 7:00 hours:
At 7:00 hours, the minute hand points at 12, while the hour hand points directly at 7. The angle between the hour hand and the minute hand is 7 * 30 - 0 * 6 = 210 degrees.
so this option is not correct.
(b) Between 7:00 hours and 7:05 hours:
During this time interval, the minute hand moves from 12 to a position between 1 and 2 (approximately). However, the hour hand remains pointing directly at 7. Therefore, the angle between the hour hand and the minute hand is greater than 180 degrees.
This option is not correct.
(c) At 7:05 hours:
At 7:05 hours, the minute hand points at 1, while the hour hand is slightly past 7, moving towards 8. The angle between the hour hand and the minute hand is approximately
7.25 * 30 - 1 * 6 = 217.5 - 6 = 211.5 degrees.
so this option is not correct.
A little after 7:05 ,hour and minute hand will be 180 degree apart.So option (d) is correct
- Joseph visits the club on every 5th day, Harsh visits on every 24th day, while Sumit visits on every 9th day. If all three of them met at the club on a Sunday, then on which day will all three of them meet again?(2021)
(A) Monday
(B) Wednesday
(C) Thursday
(D) Sunday
Answer-B
To find the day on which Joseph, Harsh, and Sumit will meet again, we need to find the least common multiple (LCM) of their visiting days.
Joseph visits the club every 5th day,
Harsh visits every 24th day,
Sumit visits every 9th day.
LCM of 5, 24, and 9 is 360.
Therefore, Joseph, Harsh, and Sumit will meet again 360 days after sunday
We don't have to count all the 360 days ,instead we use the concept of odd days.
Odd number of days in 360 = Remainder of 360/7 , which is 3
Sunday + 3 = Wednesday is the right answer.
- From January 1, 2021, the price of petrol (in Rupees per litre) on mth day of the year is 80 + 0.1m, where m = 1, 2, 3, ..., 100 and thereafter remains constant. On the other hand, the price of diesel (in Rupees per litre) on the nth day of 2021 is 69 + 0.15n for any n. On which date in the year 2021 are the prices of these two fuels equal?(2021)
(A) 21st May
(B) 20th May
(C) 19th May
(D) 18th May
Answer-B
Price of the diesel on nth day of the year = 69 + 0.15n
Price of the petrol on mth day of the year = 80 + 0.1m
Where m = 1 to 100. After which it remains constant.
So The price of the petrol on and after 100th day = 80 + 0.1 × 100 = 80 + 10 = Rs. 90
Now, total number of days till 30th April = 31 + 28 + 31 + 30 = 120 days
Let’s consider the options.
Consider Option (1):
21st May means 120 + 21 = 141 days
Price of the diesel = 69 + 0.15 × 141 = 90.15
Therefore, we can say that on 21st May 2021 price of these two fuels is not equal.
Consider Option (2):
20th May means 120 + 20 = 140 days
Price of the diesel = 69 + 0.15 × 140 = 90
Therefore, we can say that on 20th May 2021, the price of these two fuels will be equal.
Therefore option (2) is the correct answer.
- How many seconds in total are there in x weeks, x days, x hours, x minutes and x seconds?(2022)
(A) 11580x
(B) 11581x
(C) 694860х
(D) 694861x
Answer-D
To calculate the total number of seconds in x weeks, x days, x hours, x minutes, and x seconds, we need to convert each unit to seconds and then add them together.
1 week = 7 days
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds
So, the conversion factors are as follows:
1 week = 7 * 24 * 60 * 60 seconds
1 day = 24 * 60 * 60 seconds
1 hour = 60 * 60 seconds
1 minute = 60 seconds
Now, let's calculate the total number of seconds:
Total seconds = (x weeks * 7 * 24 * 60 * 60) + (x days * 24 * 60 * 60) + (x hours * 60 * 60) + (x minutes * 60) + x seconds
Simplifying the equation, we get:
Total seconds = x * (7 * 24 * 60 * 60 + 24 * 60 * 60 + 60 * 60 + 60 + 1)
By further simplifying, we find that the total number of seconds is:
Total seconds = x * 694861
Therefore, the correct option is (d) 694861x.
- A man started from home at 14:30 hours and drove to the village, arriving there when the village clock indicated 15:15 hours. After staying for 25 minutes, he drove back by a different route of length 1.25 times the first route at a rate twice as fast, reaching home at 16:00 hours. As compared to the clock at home, the village clock is(2022)
(A) 10 minutes slow
(B) 5 minutes slow
(C) 10 minutes fast
(D) 5 minutes fast
Answer-D
Total time taken by the man to come back home = 16 – 14.5 = 1.5 hours = 60 + 30 = 90 minutes
Time stayed in the village = 25 minutes.
So, total traveling time = 90 – 25 = 65 minutes
The length of the return route was 1.25 times the length of initial route.
So, time taken increased by 25% too.
So, if the initial time was 100 units, now it must be 125 units.
But while returning he drove twice as fast.
So, time taken becomes half
So, time taken while returning back = 125/2 = 62.5 units
So, 100 + 62.5 Or 162.5 units = 65 minutes
So, 100 units = (65/162.5) × 100 = 40 minutes
So, the man took 40 minutes to reach the village.
So, the actual time at that moment = 14:30 + 40 minutes = 15:10 hours
Therefore the village clock is 15:15 – 15:10 = 5 minutes fast
- Consider the following statements:
- Between 3:16 p.m. and 3:17 p.m., both hour hand and minute hand coincide.
- Between 4:58 p.m. and 4:59 p.m., both minute hand and second hand coincide.
Which of the above statements is/are correct?(2022)
(A) 1 only
(B) 2 only
(C) Both 1 and 2
(D) Neither 1 nor 2
Answer-C
Let's consider statement 1:
At 3 o’clock, the minute hand is 15 minutes apart from the hour hand.
To coincide, it must gain 15 minute spaces.
So, 15 minutes are gained in
(60/55) × 15 = 180/11 minutes = 16.36 minutes
Thus,the hour hand and the minute hand will coincide at 3:16:36, which is between 3:16 pm and 3:17 p.m.
Therefore statement 1 is correct.
Let's Consider statement 2:
At 4:58 p.m. the second hand is at 12.
In the next minute, it will definitely cross the minute hand.
Thus, between 4:58 p.m. and 4:59 p.m. the minute hand and second hand will coincide.
statement 2 is also correct.
So,both statements are correct.
