๐
= 30(H) - \({11 \over {2}}\) (M)

= 30(7) - \({11 \over {2}}\) (40)

= 210 - 220 = |- 10ห |= 10ห Hence (a).

= 30(7) - \({11 \over {2}}\) (40)

= 210 - 220 = |- 10ห |= 10ห Hence (a).

By what angle will the hour hand rotate between 8: 30 a.m. and 9: 55 a.m.?

The speed of the hour hand =ย \({1 \over {2}}ห\) per minute

Total time = 85 minutes

So, the hour hand will rotate through =ย \({85 \over {2}}\) = 42.5 ห .ย Hence (b).

๐
= \({11 \over {2}}\) (M) - 30(H)

110 ห = \({11 \over {2}}\) (M ) - 30(2)

110 + 60 = \({11 \over {2}}\) (M)

M = 30\({10 \over {11}}\)

Required time = 2: 30\({10 \over {11}}\) . Hence (d).

110 ห = \({11 \over {2}}\) (M ) - 30(2)

110 + 60 = \({11 \over {2}}\) (M)

M = 30\({10 \over {11}}\)

Required time = 2: 30\({10 \over {11}}\) . Hence (d).

In clock, a ll angles except 0 ห and 180 ห are formed 22 times in 12 hours. Hence (c).

๐
= 30(H) - \({11 \over {2}}\) (M)

= 30(8 ) - \({11 \over {2}}\) (16 )

= 240 - 88 = 152 ห

Reflex angle = 360 โ 152 = 208ห . Hence (b).

= 30(8 ) - \({11 \over {2}}\) (16 )

= 240 - 88 = 152 ห

Reflex angle = 360 โ 152 = 208ห . Hence (b).

Speed of the minute hand = 6 ห per minute

To travel 234 ห it will take 39 minutes

Speed of the hour hand = \({1 \over {2}}ห\) per minute

For 39 minutes it will move 19.5 ห . Hence (c).

To travel 234 ห it will take 39 minutes

Speed of the hour hand = \({1 \over {2}}ห\) per minute

For 39 minutes it will move 19.5 ห . Hence (c).

A asked a girl, โWhat is the time now?โ. The girl replied that the time left is 1/11^{th} of the time already completed in that day. What is the exact time?

Let the time completed be x hours. Time left = 24 โ x = \({x \over {11}}\) ร x = 22 hours The exact time => 10 p.m. Hence (b).

At 6 oโ clock it rings 6 times.

Time lapse between the two rings = \({55 \over {5}}\) = 11

At 10 oโ clock, it rings 10 times. After first ring, the clock will ring 9 times.

Required time = 9 *11 = 99 seconds. Hence (c).

Time lapse between the two rings = \({55 \over {5}}\) = 11

At 10 oโ clock, it rings 10 times. After first ring, the clock will ring 9 times.

Required time = 9 *11 = 99 seconds. Hence (c).

The minute hand takes one hour to cover 360 ห .

For 6480 ห it travels 18 hours and time will be 5 p.m.

๐ = 30(H) - \({11 \over {2}}\) (M)

๐ = 30(5) - \({11 \over {2}}\) (0) = 150ห . Hence (d).

For 6480 ห it travels 18 hours and time will be 5 p.m.

๐ = 30(H) - \({11 \over {2}}\) (M)

๐ = 30(5) - \({11 \over {2}}\) (0) = 150ห . Hence (d).

A clock was set right at 11 a.m. on a Saturday. It loses 3% time during the first week and gains 6% in the next week. After 14 days, what will be the time that the clock will show from the time was set right?

There are 7 * 24 = 168 hours in a week. If the clock loses 3% time during the first week, then it will show 3% of 168 hours less than 11 a.m. at the end of the first week ร 5.04 hours less After that, the clock gains 6% during the next week. The second week has 6% of 168 hours ร more than the actual time. ร 10.08 hours more It lost 5.04 hours during the first week and then gained 10.08 hours during the next week, net gain = - 5.04 + 10.08 = 5.04 hours gain in time. Clock will show a time which is 5.04 hours more than 11 a.m. two weeks from the time it was set right. 5.04 hours = 5 hours 2 minutes 24 seconds. Hence (a).

The clock was 8 minutes late at 2pm on Thursday and 8 minutes ahead at 4 pm on Satur day

Thus, the clock has gained 16 minutes in 10(from Thursday after 2 pm) + 24(complete Fr iday) + 16 ( 12 p m to 4 pm on Satur day) = 50 hours

S o 8 minutes will be gained in (8/16)*50 = 25 hours

Thus the clock will show the correct time at near about 3 : 00 pm on Fri day. He nce (d).

Thus, the clock has gained 16 minutes in 10(from Thursday after 2 pm) + 24(complete Fr iday) + 16 ( 12 p m to 4 pm on Satur day) = 50 hours

S o 8 minutes will be gained in (8/16)*50 = 25 hours

Thus the clock will show the correct time at near about 3 : 00 pm on Fri day. He nce (d).

At exactly 3 oโ clock the hour hand is 15 minutes spaces ahead of the minute hand.

To be 1 8 minute spaces apart, the minute hand has to gain (15 + 18) = 3 3 minute spaces over the hour hand.

In 1 hour 55 minute spaces are gained.

For gaining 3 3 minute spaces = \({60 \over {55}}\) * 3 3 = 36 minutes.

Required time = 3: 36 . Hence (c).

To be 1 8 minute spaces apart, the minute hand has to gain (15 + 18) = 3 3 minute spaces over the hour hand.

In 1 hour 55 minute spaces are gained.

For gaining 3 3 minute spaces = \({60 \over {55}}\) * 3 3 = 36 minutes.

Required time = 3: 36 . Hence (c).

An inaccurate clock shows 6 p.m. and the clock gains 8 minutes for every 12 hours. If the actual time shows 7 p.m. on the 5^{th} day, then what time will the clock show?

Time from 6 p.m. on the first day to 7 p.m. on the fifth day = 97 hours

For every 12 hours clock gains 8 minutesย

For every 1 hour 8/12 = 2/3 minutes gain

Total gain from 1 ^{st} day to at 6 p.m. toย 5 ^{th} day 7 p.m. => 97 *ย \({2 \over {3}}\) ย = 64.6 minutes gain

So, when the actual time is 7 p.m. the clock shows 8: 05 p.m. ย Hence (a).

A clock is set right at 7 a.m. in the morning. It gains 4 seconds every 15 minutes. If the actual time is 4 p.m. on the same day, find the angle between the hour hand and the minute hand the clock shows.

Clock gains 4 seconds in every 15 minutes. So in one hour, it gains 16 seconds. From 7 a.m. to 4 p.m. ร 9 hours The clock gains 144 seconds, i.e. \({12 \over {5}}\) minutes ๐ = 30(H) ~ \({11 \over {2}}\)(M) = 30(4) ~ \({11 \over {2}}\)(\({12 \over {5}}\)) = 120 โ 13.2 = 106.8ห Hence (b).

Meenuโs office time is 9: 30 a.m. to 6: 30 p.m. One day, Meenu works overtime. When she reaches home, her watch shows a reflex angle of 200ห. During the extended hours of work, the minute hand rotates three full cycles. At what time does Meenu reach home?

Reflex angle = 200ห, Normal angle = 360ห - 200ห = 160ห Office ends at 6: 30 p.m. Extended time is 3 hours (since the minute hand rotates three full cycles) and she left office at 9: 30 p.m. 160 = 30(9) ~ \({11 \over {2}}\)(M) \({11 \over {2}}\)(M) = 110 ร M = 20 minutes Meenu reaches home at 9: 50 p.m. Hence (d).