Question

On what dates of October, 1975 did Tuesday fall ?

• A. $7^{th},{14}^{th},{21}^{st},{28}^{th}$
• B. $1^{st},8^{th},{15}^{th},{22}^{st},{29}^{th}$
• C. $2^{nd},9^{th},{16}^{st},{23}^{rd},{30}^{th}$
• D. $3^{rd},{10}^{th},{17}^{st},{24}^{th},{31}^{st}$

Answer 1

The correct option is A $7^{th},{14}^{th},{21}^{st},{28}^{th}$

For determining the dates, we find the day on 1st Oct, 1975.
$1600$ years have '0' odd days ............(A).
$300$ years have '01' odd days ............(B).
$74$ years have (18 leap years + 56 ordinary years)
$2\times 18+1\times 56=92$ odd days = '01' odd days.....(C)
Days from 1st January to 1st Oct., 1975
1st Jan - 30 June + 1st July to 1st Oct.
$181+31+31+30+1=274$ days $

$=\cfrac {274}{7} = '01'$ odd days................... (D)

Adding (A) + (B) +(C) +(D) $=0+01+01+01$
${=}^{\prime }{03}^{\prime }$ odd days
Ans. Wednesday( 1st Oct), hence $7^{th},{14}^{th},{21}^{st},{28}^{th}$ Oct. will fall on Tuesday.