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OTI365 - NTSE - X Standard
NTSE Mental Ability Test - Problems on Clocks Sample Questions with Answer

NTSE Mental Ability Test - Problems on Clocks

Exam Duration: 45 Mins Total Questions : 30

1 )

At what time between 4 o'clock 6- 5 o'clock, will the hands of a clock be together?

(a)
22 \(\frac{9}{11}\) min past 4
(b)
21 \(\frac{9}{11}\)min past 4
(c)
27 \(\frac{3}{11}\) min past 4
(d)
21 \(\frac{3}{11}\) min past 4

Solution :

Minute hand will have to cover 20 minutes to be together with hour hand therefore \((\frac{60}{50}\times 20)=21 \frac{9}{11}\) minutes past 4 or by shortcut method = \((\frac{60\times4}{11})=21 \frac{9}{11}\) past 4.

2 )

At what time between 9 o'clock & 10 o'clock, will the hands of a clock be together?

(a)
51 \(\frac{1}{11}\) min past 9
(b)
49 \(\frac{1}{11}\) min past 9
(c)
49 \(\frac{10}{11}\) min past 9
(d)
50 \(\frac{10}{11}\) min past 9

Solution :

Minute hand will have to cover 45 minutes to be together with hour hand, therefore \((\frac{60}{55}\times 45)=49 \frac{1}{11}\) minutes past 9 or by shortcut method \(=(\frac{60\times9}{11})=49 \frac{1}{11}\)

3 )

At what time between 7:30 o'clock & 8 o'clock the hands of the clock will be 10 o'clock apart?

(a)
20 min past 7
(b)
55\(\frac{6}{11}\) min past 7
(c)
56 \(\frac{9}{11}\) min past 7
(d)
56 \(\frac{4}{11}\) min past 7

Solution :

100 =\(\frac{11m-60\times 7}{2} = 56 \frac{4}{11}\) past 7

4 )

At what time between 6 o'clock & 7 o'clock the hands of the clock will be inclined at 60· for the first time?

(a)
21 \(\frac{9}{11}\) min past 6
(b)
43 \(\frac{7}{11}\) min past 6
(c)
21 \(\frac{7}{11}\) min past 6
(d)
43 \(\frac{9}{11}\) min past 6

Solution :

60 =\(\frac{60\times6-11m}{2} = 21 \frac{9}{11}\) past 6

5 )

When the time by clock is 20 minutes past 4 o'clock, the angle between hands of the clock will be

(a)
5⁰
(b)
10⁰
(c)
12⁰
(d)
15⁰

Solution :

Angle = \(\frac{60\times4-11\times20}{2}=10\)

6 )

The time by watch is 15 minutes to 5'0 clock; find the angle between the hands of the clock?

(a)
125.5⁰
(b)
127.5⁰
(c)
132.5⁰
(d)
125⁰

Solution :

Angle = \(\frac{46\times11-60\times4}{2}=127.5\)

7 )

A mirror is placed in front of a clock, if time shown by clock in the mirror is 11:20, then what will be the actual time shown by the clock?

(a)
3:55
(b)
12:40
(c)
12:20
(d)
1:20

Solution :

12:40

8 )

A minute hand of a clock overtakes the hour handat intervals of 65 min of the correct time. How much does a clock gain or lose in a day?

(a)
2 hr 10 \(\frac{10}{11}\)min
(b)
2 hr 11 \(\frac{10}{11}\)min
(c)
2 hr \(\frac{10}{11}\)min
(d)
2 hr \(\frac{6}{11}\)min

Solution :

We know that in a correct clock two hands of the clock coincides after every 65 \(\frac{5}{11}\) minutes, but as per question, here minutes hand overtakes hour hand in 60 minutes
Therefore gain in 60 minutes = 65 \(\frac{5}{11}\)-60=5\(\frac{5}{11}\)
In 60 minutes hand gains 5 \(\frac{5}{11}\) minutes
So in 24 hours it will gain = \(\frac{24\times60}{11}=130\frac{10}{11} \)min = 2 hour 10\(\frac{10}{11}\) min

9 )

A Clock is set to show correct time at 10:00 AM,if it loses 25 minutes every day. What will be the timein minutes it will lose by 4:00 PM next day?

(a)
32 34 min
(b)
31 14 min
(c)
30 14 min
(d)
28 34 min

Solution :

In 24 hours clock will lose 25 min
In 1 hour it will lose 25/24 min
In 30 hours (10:00 AM to 4:00 PM next day) it will lose = \(\frac{(30\times25)}{24}=31\frac{1}{4}\)min

10 )

What is the day on 1^st January 1901?

(a)
Monday
(b)
Wednesday
(c)
Sunday
(d)
Tuesday

Solution :

1^st January 1901 means (1900 years and 1day)
Now, 1600 years have 0 odd days
300 years have 1 odd day
1day has 1 odd day
Total number of odd days = 0 + 1+ 1= 2 days
Hence, the day on 1^st January 1901 was Tuesday.

11 )

The year next to 1990 will have the same calendar as that of the year 1990 is:

(a)
1995
(b)
1996
(c)
1997
(d)
1999

Solution :

The year 1990 has 365 days i.e. 1 odd day, year 1991 has 365 days i.e. 1 odd day, year 1992 has 366 days i.e. 2 odd days.
Likewise, years 1993, 1994, 1995, have 1 odd day each. The sum of odd days so calculated from year 1990 to 1995(1 + 1 + 2 + 1 + 1 + 1) = 7 odd days ≡ 0 odd day.
Hence, the year 1996 will have the same calendar as that of the year 1990.

12 )

How many times in a day, the hands of a clock are straight?

(a)
22
(b)
24
(c)
44
(d)
48

Solution :

In 12 hours, the hands coincide or are in opposite direction 22 times.
In 24 hours, the hands coincide or are in opposite direction 44 times a day.

13 )

On what dates of April, 2001 did Wednesday fall?

(a)
1^st, 8^th, 22^nd,29^th
(b)
2^nd, 9^th, 16^th, 23^rd, 30^th
(c)
3^rd, 10^th, 17^th, 24^th
(d)
4^th, 11^th, 18^th, 25^th

Solution :

We shall find the day on 1^stApril, 2001.
1^stApril, 2001 = (2000 years + Period from 1.1.2001 to 1.4.2001)
Odd days in 1600 years = 0
Odd days in 400 years = 0
Jan. Feb. March April
(31 + 28 + 31 + 1) = 91 days ≡ 0 odd days.
Total number of odd days = (0 + 0 + 0) = 0
On 1^stApril, 2001 it was Sunday.
In April, 2001 Wednesday falls on 4^th, 11^th, 18^thand 25^th

14 )

The calendar for the year 2007 will be the same for the year:

(a)
2014
(b)
2016
(c)
2017
(d)
2018

Solution :

Count the number of odd days from the year 2007 onwards to get the sum equal to 0 odd day.
Year Odd day
2007 1
2008 2
2009 1
2010 1
2011 1
2012 2
2013 1
2014 1
2015 1
2016 2
2017 1
Sum = 14 odd days ≡ 0 odd days.
∴ Calendar for the year 2018 will be the same as for the year 2007.

15 )

January 1, 2008 is Tuesday. What day of the week lies on Jan 1, 2009?

(a)
Monday
(b)
Wednesday
(c)
Thursday
(d)
Sunday

Solution :

The year 2008 is a leap year. So, it has 2 odd days.
1^stday of the year 2008 is Tuesday (Given)
So, 1^st day of the year 2009 is 2 days beyond Tuesday.
Hence, it will be Thursday.

16 )

January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008?

(a)
Monday
(b)
Tuesday
(c)
Wednesday
(d)
Sunday

Solution :

The year 2007 is an ordinary year. So, it has 1 odd day.
1^st day of the year 2007 was Monday.
1^st day of the year 2008 will be 1 day beyond Monday.
Hence, it will be Tuesday.

17 )

A clock is started at noon. By 10 minutes past 5, the hour hand has turned through:

(a)
145⁰
(b)
150⁰
(c)
155⁰
(d)
160⁰

Solution :

Angle traced by hour hand in 12 hrs = 360°.
Angle traced by hour hand in 5 hrs 10 min. i.e. 31/6 hrs
= (360/12 \(\times\) 31/6) ° = 155°

18 )

Find the day of the week on 26 January, 1950.

(a)
Tuesday
(b)
Friday
(c)
Wednesday
(d)
Thursday

19 )

If it was Saturday on 17th November 1962 what will be the day on 22nd November 1964?

(a)
Monday
(b)
Tuesday
(c)
Wednesday
(d)
Sunday

20 )

If the seventh day of a month is three days earlier than Friday, what day will it be on the nineteenth day of the month?

(a)
Sunday
(b)
Monday
(c)
Wednesday
(d)
Friday

21 )

If 27th January. 1996 was Sunday then what day would be on 26th March 1997?

(a)
Monday
(b)
Tuesday
(c)
Thursday
(d)
Sunday

22 )

The year that will have the same calender as that of the year 1995 is

(a)
2002
(b)
2005
(c)
2006
(d)
2001

23 )

If it was Saturday on 17th December, 1982 what will be the day of 22nd December 1984?

(a)
Monday
(b)
Tuesday
(c)
Wednesday
(d)
Sunday

24 )

If the day before yesterday was Saturday, what day will fall on the day after tomorrow?

(a)
Friday
(b)
Thursday
(c)
Wednesday
(d)
Tuesday

25 )

At what time between 6 and 7 O' clock the hands of a clock will be at right angle?

(a)
\(16\frac{4}{11}\) minutes past 6
(b)
\(16\frac{3}{4}\) minutes past 6
(c)
\(49\frac{1}{11}\) minutes 6
(d)
33 minutes past 6

26 )

A bus for Delhi leaves every thirty minutes from a bus stand. An enquiry clerk told a passenger that the bus had already left ten minutes ago and the next bus will leave at 9.35 a.m. At what time did the enquiry clerk give this information to the passenger?

(a)
9.10 am
(b)
8.55 am
(c)
9.05 am
(d)
9.15 am

27 )

A clock is set right at 1 pm. The clock loses 12 minutes in 24 hours. What time will the clock show when the true time is 9 pm on the 3^rd day?

(a)
8: 28 pm
(b)
8: 32 pm
(c)
8: 22 pm
(d)
9: 28 pm

28 )

At what time are the hands of a clock together between 5 and 6?

(a)
\(33\frac{3}{11}\) min. past 5
(b)
\(28\frac{3}{11}\) min. past 5
(c)
\(27\frac{3}{11}\) min. past 5
(d)
\(26\frac{3}{11}\) min. past 5

29 )

There are twenty people working in an office. The first group of five works between 8.00 A.M. and 2.00 P.M. The second group of ten works between 10.00 A.M. and 4.00 P.M. And he third group of five works between 12 noon and 6.00 P.M. There are three computers in the office which all the employees frequently use. During which of the following hours the computers are likely to be used most?

(a)
10.00 A.M. - 12 noon
(b)
12 noon - 2.00 P.M
(c)
l.00 P.M. - 3.00 P.M.
(d)
2.00 P.M. - 4.00 P.M.

30 )

A 12 dial clock has its minutes hand defective. Whenever it touched, dial 12, it immediately falls down to 6 instead of running smoothly (the hour hand remains unaffected during that fall). It was set right at 12 'O' clock in the noon.
What was the actual time when the minute hand of the clock touched dial 9 for the 5^th time?

(a)
2: 15
(b)
3:00
(c)
5: 15
(d)
6: 45