11.
A can run 500 m in 30 sec and B in 35 sec. How many m start can A give to B in a km race so that the race may end in a dead-heat?
•  A.139 5 7
•  C.142 6 7
•  B.138 5 7
•  D.140 5 7
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Explanation :

Time taken by A to run 1 km = 30 x 2 = 60 sec.

Time taken by B to run 1 km = 35 x 2 = 70 sec.

A can give B a start of (70 - 60) = 10 sec.

 In 35 sec B runs 500 m

In 10 sec B runs =
 500 35
x 10 =
 1000 7
= 142
 6 7
m

So, A can give B a start of 142
 6 7
metres in a km race.

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12.
In a km race A beats B by 100 m and C by 200 m, by how much can B beat C in a race of 1350 m?
• A.
150 m
• C.
1200 m
• B.
120 m
• D.
210 m
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Explanation :

While A runs 1000 m, B runs 1000 – 100 = 900 m and C runs 1000 – 200 = 800 m.

While B runs 900 m, C runs 800 m.

While B runs 1350 m; C runs
 800 900
x 1350 = 1200 m

B can beat C by 1350 - 1200 = 150 m.

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13.
In a race of 600 m, A can beat B by 60 m and in a race of 500 m, B can beat C by 50 m. By how many m will A beat C in a race of 400 m?
• A.
78 m
• C.
76 m
• B.
56 m
• D.
86 m
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Explanation :

If A runs 600 m, B runs 600 – 60 or, 540 m

If A runs 400 m, B runs  =
 540 x 400 600
= 360 m

Now, when B runs 500 m, C runs 500 – 50 = 450 m

When B runs 360 m, C runs =
 450 x 360 500
= 324 m

A beats C by 400 - 324 = 76 m.

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14.
In a 300 m race A beats B by 22.5 m or 6 seconds. B’s time over the course is :
• A.
86 sec
• C.
76 sec
• B.
80 sec
• D.
None of these
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Explanation :

B runs
 45 2
m in 6 sec.

B covers 300 m in   6 x
 2 45
x 300    sec = 80 sec.

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15.
In a km race A beats B by 25 m or 5 sec, find the time taken by A to complete the race.
• A.
3 min. 15 sec
• C.
2 min 30 sec
• B.
4 min. 20 sec
• D.
5 min. 10 sec
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Explanation :

B runs 25 m in 5 sec

B's time to cover one km =
 5 25
x 100

 = 200 sec

 A's time to cover one km = 200 - 5

 = 195 sec

 = 3 min 15 sec.

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