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Shortcut 87:
                             Using the odd days
Question:
Find the day of birth of MS Dhoni (7 July, 1981), if 31 Dec 1999 is Friday
Answer:
Days after 7/7/1981 in 1981 = 177
Odd days by normal years from 1982 to 1999 = 14
Odd days by leap years = 4 x 2 = 8
Total odd days = 177 + 14 + 8 = 199
Remainder of 199/7 = 3
Since last day is Friday, MSD’s birth day is 3 days before Friday,
MSD’s day of birth = Tuesday.

Clocks
Shortcut 88:
Minute hand and Hour hand overlapping

\(\frac{60h}{11}\)

Question:
At what time between 3pm and 4pm, the hour hand and the minute hand will be overlapping?
Answer:
h = starting time = 3
Time at which the hands will be overlapping,
= (60 x 3)/11
= 180/11
= 16.36 minutes after 3pm
= 03h 16m 21s

Shortcut 89:
Two hands at angleƟ
  12/11(5h\(\pm\)0/6)
Question:
At what times between 1pm and 2pm the hour hand and minute hand will be 30 degrees apart?
Answer:
h = 1
Ɵ = 30
Substitute the values in the above formula, we get
(12/11)[(5 x 1) ± (30/6)]
= (12/11)(5 + 5) , (12/11)(5 – 5)
= 10.9 minutes past 1, 0 minutes past 1
= [01h 10m 54s] and [01h 00m 00s]

Shortcut 90:
Two hands M minutes apart
\(\frac{12}{11}(5h\pm M)\)
Question:
At what times between 5pm and 6pm the hour hand and minute hand will be 10 minutes apart?
Answer:
h = 5
M = 10
Substitute the values in the above equation, we get
(12/11)[(5 x 5) ± 10]
= (12/11)(25+10) and (12/11)(25 – 10)
= 38.18 minutes past 5 and 16.36 minutes past 5
= [05h 38m 10s] and [05h 16m 20s]