Answer: Option B. -> 56 $8/77$ min (gain)
Answer: (b)
Method I
As we know that in a correct clock, the minute hand gains 55 min spaces over the hour hand in 60 min.
To be together again, the minute hand must gain 60 min over the hour hand.
60 min are gained in $(60/55 × 60) min = 65 5/11 min$
But they are together after 63 min.
Therefore, gain in 63 min =$ (65 5/11 - 63) = 2 5/11 min = 27/11 min$
Gain in 24 h = $(27/11 × 60 × 24/63) min = 4320/77 min = 56 8/77 min$
As result is positive, therefore clock gains 56 $8/77$ min.
Method II
In the given question, x = 63 min
According to the formula,
Required result = $(720/11 - x) (60 × 24 /x) min = (720/11 - 63) (60 × 24 /63 ) min$
= $27/11 × 60 × 8 /21 = 56 8/77 $min (gain as sign in positive)

Answer: Option D. -> 2 p.m. on Wednesday
Answer: (d)
Time from 12 p.m. on Monday to 2 p.m.
on the following Monday = 7 days 2 hours = 170 hours.
Therefore, the watch gains $(2 + 4 4/5) min. or 34/5 min.$ in 170 hrs.
now, 34/5 min. are gained in 170 hrs.
2 min. are gained in $(170 × 5/34 × 2) hrs = 50 hrs.$
Therefore, Watch is correct 2 days 2 hrs. after 12 p.m. on Monday
i.e. it will be correct at 2 p.m. on Wednesday

Answer: Option C. -> 445 $5/55$ min (gain)
Answer: (c)
Required result = $(720/11 - x) (60 × 24 /x) min$
Here, x = 50 Therefore, required result = $(720/11 - 50) (60 × 24/50) min$
= $(170/11 × 144/5) min$
= 445 $5/55$ min gain (gain as sign is positive)

Answer: Option A. -> 24 minutes past 5
Answer: (a)
Since the time read by the lady was 57 minutes earlier than the correct time,
so the minute hand is (60 - 57) = 3 minute spaces behind the hour hand.
Now, at 5 O' clock, the minute hand is 25 minute spaces behind the hour hand.
To be 3 minute spaces behind, it must gain (25 - 3) = 22 minute spaces.
55 min spaces are gained in 60 min.
22 min spaces are gained in $(60/55 × 22) = 24 min$
Hence, the correct time was 24 minutes past 5.

Answer: Option A. -> 368 $112/121$ min (loss)
Answer: (a)
Required result = $(720/11 - x) (60×24 /x) min$
Here, x = 88
Therefore, required result =$ (720/11 - 88) (60×24 /88) min$
= $-248/11 × 180/11 min = -368 112/121 min$ (loss as sign in negative)

Answer: Option D. -> 4 p.m.
Answer: (d)
Time from 7 a.m. to 4.15 p.m. = 9 hrs 15 min = $37/4$ hrs 3 min 5 sec of this clock = 3 min. of the correct clock.
= $37/720$ hrs of this clock = $1/20$ hrs of the correct clock
= $37/4$ hrs of this clock
= $(1/20 × 720/37 × 37/4)$ hrs of the correct clock
= 9 hrs of the correct clock
Therefore, The correct time is 9 hrs after 7 a.m., i.e. 4 p.m.