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'