LTI Clocks and Calendar Quiz-1

On 31st December, 2021 it was Friday
Number of odd days from the year 2022 to the year 2026 = (1 + 1 + 2 + 1) = 5 days.
On 31st December 2025, it was Wednesday.
Thus, on 1st Jan, 2026 it is Thursday

1 century = 100 years =(76 ordinary years + 24 leap year)
(no. of odd days in ordinary year = 1
no. of odd days in leap year = 2)
So, (76 × 1 + 24× 2)odd day
= 124 odd days
= 17 weeks + 5 odd days
= 5 odd days
Number of odd days in 200 years = (5 x 2) =10 = 3 odd days.
Number of odd days in 300 years = (5 x 3) =1 odd day.
Number of odd days in 400 years = (5 x 4 + 1) =0 odd day.
Similarly, each one of 800 years, 1200 years, 1600 years, 2000 years , 2400 etc. has 0 odd days.

The clock has totally gained 16 minutes and 40 sec. i.e. 1000 seconds in 160 hrs.
In order to show the right time, the clock has to gain only 6 min i.e. 360 seconds.
Just apply the chain rule,
the clock gained 1000 sec in 160 hrs.
It will gain 360 sec. in 360 × 160/1000 = 288/5 hrs i.e. 57 3/5.
Adding 57 hrs & 36 minutes in Monday 5 p.m. we get-
2:36 a.m. on Thursday.

We know that angle between two hands is given by
\theta =\left | \frac{11}{2} M- 30H\right |^{\circ}
⇒ \theta =\left | \frac{11}{2}\times 38- 30\times 5\right |^{\circ}=59^{\circ}

According to the question, 10th March is Friday.
Number of days left in March = 31 – 10 = 21.
Similarly, odd days from 10th March till 25th September = (21 + 30 + 31 + 30 + 31 + 31 + 25) % 7 = 0 + 2 + 3 + 2 + 3 + 3 + 4 = 17/7.
Remainder = 3.
Thus, day on 25th September = Friday (+3) = Monday.
Hence, Anushka's birthday will be on Monday.

Number of odd days in 2013 year = Remainder of (365 ÷ 7)=1 So, on 5 February 2014, the day would be → 5 February 2013 +1

Sunday + 1

Monday

According to the question, 12th April is Wednesday.
Number of days left in April = 30 – 12 = 18.
Similarly, odd days from 12th April till 2nd October = (18 + 31 + 30 + 31 + 31 + 30 + 2) / 7
= (4 + 3 + 2 + 3 + 3 + 2 + 2)/7 = 19/7 = 5
Thus, day on 2nd October = Wednesday + 5 = Monday.

7 seconds lost every hour for 4 days = 7 seconds lost every hour for (24*4) hours = 7 seconds lost every hour for 96 hours = (7*96) seconds lost = 672 seconds lost = (672/60) minutes lost = 11.2 minutes lost

When we divide 44 by 7 we get as 2 remainder
So, 44-2= 42
After 42nd day it will Friday again
On 43rd day Saturday
On 44th day Sunday

In a span of 12 hrs, the hands of a clock are at right angles exactly 22 times.
So, in a span of 48 hrs, they are at right angles exactly 88 times.