Question:In a game of 80 points, A can give B 5 points and C 15 points. Then how many points B can give C in a game 60 ?
A : B = 80 : 75, A : C = 80 : 65 `B/C = (B/A xx A/C)` `= (75/80 xx 80/65)` `= 15/13 = 60/52 = 60 : 52` :. In a game of 60, B can give C 8 points.
Question:Find the day of the week on 6th July, 1776.
(i) 16th july, 1776 means
= (1775 years + period from 1st January to 16th July)
Now, 1600 years have 0 odd day.
100 years = (18 leap years + 57 ordinary years)
= (36 + 57) odd days = 93 odd days
= (13 weeks + 2 days) of odd days
= 2 odd days.
:. 1775 years have (0 + 5 + 2) odd days i,e 0 odd days.
Now, days from 1st Jan, 16th July ; 1776
Jan Feb March April May June July
31 + 29 + 31 + 30 + 31 + 30 + 16 = 198 days
= (28 weeks + 2 days) = 2 odd days.
:. Total number of odd days = (0 + 2) = 2.
:. The day of the week was ' Tuesday'Question:What was the day of the week on 12th January, 1979 ?
Number of odd days in (1600 + 300) years = (0 + 1) = 1.
78 years = (19 leap years + 59 ordinary years)
= (38 + 59) odd days = 97 odd days = 6 odd days.
12 days of January have 5 odd days.
:. Total number of odd days = (1 + 6 + 5) = 5 odd days.
:. The desired day was 'Friday'.Question:Find the day of the week on 25th December, 1995.
1600 years have 0 odd day. 300 years have 1 odd day. 94 years = (23 leap years + 71 ordinary years) = (46 + 71) odd days = 117 odd days = 5 odd days. Number of days from 1st Jan, 1995 to 25 th Dec, 1995 = 359 days. = (51 weeks + 2 days) = 2 odd days. :. Total number of odd days = (0 + 1 + 5 + 2) odd days = 1 odd day. :. Required day is 'Monday'.
Question:On what dates of October, 1994 did Monday fall ?
Find the day on 1st October, 1994. 1600 years contain 0 odd day. 300 years contain 1 odd day. 93 years = (23 leap years + 70 ordinary years) = (46 + 70) odd years = 116 odd days = 4 odd days. Days from 1st Jan, 1994 to 1st Oct, 1994 Jan Feb March April May June July Aug Sept Oct 31 + 28 + 31 + 30 + 31 + 30 + 31 + 31 + 30 + 1 = 274 days = 39 weeks + 1 days = 1 odd day. :. Total number of odd days = (0 + 1 + 4 + 1) = 6. :. 1st Oct, 1994 was 'Saturday' :. Monday fell on 3rd October, 1994. During October 1994, Monday fell on 3rd, 17th and 24 th.