From Zeller's Formula:
f = k + [13 x m - 1 / 5] + D + [D/4] + [C/4] - 2 x C.
In this case k = 15 (since 15th August)
Month m = 6 (As march = 1, April = 2, May = 3, August = 6)
D is the last two digit of year here D = 47 (As year is 1947)
C is the 1st two digit of century here C = 19 (As year is 1947)
f = 15 + [13 x 6 - 1 / 5] + 47 + [47/4] + [19/4] - 2 x 19.
f = 15 + [77/5] + 47 + [11.75] + [4.75] - 38.
f = 15 + 15 + 47 + 11 + 4 - 38 = 54.
When divided by 7 we will get remainder 5, hence number of odd days is 3,
A remainder of 0 corresponds to Sunday, 1 means Monday,
So 15th August 1947 is 5 days more than Sunday, i.e Friday.
∴ The watch gains | ❨ | 2 + 4 | 4 | ❩min. | or | 34 | min. in 170 hrs. |
5 | 5 |
Now, | 34 | min. are gained in 170 hrs. |
5 |
∴ 2 min. are gained in | ❨ | 170 x | 5 | x 2 | ❩hrs | = 50 hrs. |
34 |
∴ 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.
Perimeter = Distance covered in 8 min. = | ❨ | 12000 | x 8 | ❩m = 1600 m. |
60 |
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
∴ Length = 480 m and Breadth = 320 m.
∴ Area = (480 x 320) m2 = 153600 m2.
Also, lb = 20.
(l + b)2 = (l2 + b2) + 2lb = 41 + 40 = 81
⟹ (l + b) = 9.
∴ Perimeter = 2(l + b) = 18 cm.
Let 40% of A = | 2 | B |
3 |
Then, | 40A | = | 2B |
100 | 3 |
⟹ | 2A | = | 2B |
5 | 3 |
⟹ | A | = | ❨ | 2 | x | 5 | ❩ | = | 5 |
B | 3 | 2 | 3 |
∴ A : B = 5 : 3.
So, in a day, the hands point in the opposite directions 22 times.
∴ Last day of 1st century is Friday.
200 years contain (5 x 2) ≡ 3 odd days.
∴ Last day of 2nd century is Wednesday.
300 years contain (5 x 3) = 15 ≡ 1 odd day.
∴ Last day of 3rd century is Monday.
400 years contain 0 odd day.
∴ Last day of 4th century is Sunday.
This cycle is repeated.
∴ Last day of a century cannot be Tuesday or Thursday or Saturday.
∴ B covers 200 m in | ❨ | 7 | x 200 | ❩ | = 40 sec. |
35 |
B's time over the course = 40 sec.
∴ A's time over the course (40 - 7) sec = 33 sec.
∴ In 24 hours, they are at right angles 44 times.
T.D. |
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= Rs. 400. |
So, the day on 8th Dec, 2007 will be 1 day beyond the day on 8th Dec, 2006.
But, 8th Dec, 2007 is Saturday.
∴ 8th Dec, 2006 is Friday.
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