Question:In a km race, A beats B by 28 metres or 7 seconds. Find A'S time over the course.
Clearly, B covers 28 m in 7 seconds. :.B,s time over the course` = (7/28 xx 1000)` sec = 250 seconds. :. A's time over the course = (250 - 7) sec = 243 sec. = 4 min. 3 sec.
Question:A runs` 1 3/4` times as fast as B. If A gives B a start of 84 m,how far must the winning post be so that A and B might reach it at the same time ?
The ratio of the rates of A and B` = 7/4 : 1 = 7 : 4.` So, in a race of 7 m, A gains 3 m over B. :. 3m are gained by A in a race of 7m. :. 84 m are gained by A in a race of` (7/3 xx 84)` m = 196 m. :. Winning post must be 196 m away from the starting point.
Question:A can run 1 km in 3 min. 10 sec. and B can cover the same distance can A beat B ?
Clearly, A beats B by 10 sec. Distance covered by B in 10 sec.` = (1000/200 xx 10) m` = 50 m. :. A beats B by 50 metres.
Question:In a 100 m race, A runs at 8 km per hour. If A gives B a start of 4 m and still beats him by 15 seconds, what is the speed of B ?
Time taken by A to cover 100 m` = ((60 xx 60)/8000 xx 100) sec.`
= 45 sec.
:. B covers (100 - 4) m = 96 m in (45 + 15) sec
= 60 sec.
:. B's speed` = ((96 xx 60 xx 60)/(60 xx 1000))` km/hr = 5.76 km/hr.Question:A, B and C are three contestants in a km race. If A can give B a start of 40 m and A can give C a start of 64 m, how many metre's start can B give C ?
While A covers 1000 m, B covers (1000 - 40)m = 960 m and C covers (1000 - 64) m or 936 m. When B Covers 960 m, C covers 936 m When B covers 1000 m, C covers` (936/960 xx 1000) m` = 975 m. :. B can give C a start of (1000 - 975) or 25 m.
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.