Question: In a 200 metres race A beats B by 35 m or 7 seconds.A's time over the course is :
A
40 sec
B
47 sec
C
33 sec
D
None of these
Note: B runs 35 m in 7 sec.
:. B covers 200 m in` (7/35 xx 200)`
`= 40 sec.`
:. B's time over the course = 40 sec
A's time over the course = (40 - 7) sec
`= 33 sec.`
Question: In a 500 m race, the ratio of the speeds two contestants A and B is 3 : 4 A has a start of 140 m. Then, A wins by :
A
60 m
B
40 m
C
20 m
D
10 m
Note: To reach the winning post A will have to cover a distance of (500 - 140) m, i,e 360 m.
While A covers 3m, B covers 4 m
While A covers 360 m, B covers` ( 4/3 xx 360) m`
= 480 m.
Thus when A reaches the winning post, B covers 480 m and therefore remains 20 m behind.
:. A wins by 20 m.
Question: A runs `1 2/3` times as fast as B.If A gives B a start of 80 m, how far must the winning post be so that A and B might reach it the same time ?
A
200 m
B
300 m
C
270 m
D
160 m
Note: Ratio of the speeds of A and B` = 5/3 : 1 = 5 : 3.`
Thus in a race of 5m, A gains 2 m over B.
2m are gained by A in a race of 5m.
80 m will be gained by A in a race of` (5/2 xx 80) m.
= 200 m
:. Winning post is 200 m away from the starting point
Question: In a 100 m race, A can beat B by 25 m and B can beat C by 4 m.In the same race, A can beat C by :
A
21 m
B
26 m
C
28 m
D
29 m
Note: A : B = 100 : 75 and B : C = 100 : 96%.
:. A : C `= (A/B xx B/C)`
`= (100/75 xx 100/96)`
`= 100/72 = 100 : 72.
:. A beats C by (100 - 72) m = 28 m.
Question: In a 100 m race, A can give B 10 m and C 28 m.In the same race B can give C :
A
18 m
B
20 m
C
27 m
D
9 m
Note: A : B = 100 : 90 and A : C = 100 : 72
B : C` = B/A xx A/C`
`= 90/100 xx 100/72`
`= 90/72`
When by runs 90 m, C runs 72 m
When B runs 100 m, C runs 72 m
When B runs 100 m, C runs` (72/90 xx 100) m`
`= 80 m`
:. B can give C 20 m.
Question: In a 100 m race, A beats B by 10 m and C by 13 m.In a race of 180 m, B will beat C by :
A
5 : 4 m
B
4 : 5 m
C
5 m
D
6 m
Note: A : B = 100 : 90, A : C = 100 : 87
`B/C = B/A xx A/C `
`= 90/100 xx 100/87 = 30/29`
When B runs 180 m, C runs` (29/30 xx 180) m`
`= 174 m`
:.B beat C by (180 - 174) m = 6 m.
Question: A and B take part in a 100 m race.A runs at 5 km per hour.A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is :
A
5.15 kmph
B
4.14 kmph
C
4.25 kmph
D
4.4 kmph
Note: A's speed` = (5 xx 5/18)1` m/sec` = 25/18` m/sec.
Time taken by A to cover 100 m` = (100 xx 18/25)`sec = 72 sec.
:. Time taken by A to cover 92 m in (72 + 8) sec or 80 sec.
:. B's speed` = (92/80 xx 18/5)` kmph = 4.14 kmph