**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

*[latex]\frac{60h}{11}[/latex]
*

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[latex]\pm[/latex]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

*[latex]\frac{12}{11}(5h\pm M)[/latex]*

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]