31.
A runs 1
 3 8
times As fast as B. If A gives B a start of 120 m and they reach the goal at the
same time. The goal is at a distance of
• A.
360 m
• C.
460 m
• B.
440 m
• D.
380 m
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Explanation :

The speed of A and B are in the ratio 11 : 8.

Let speeds be 11s and 8s (in m/sec)

Let race be of x m

Then time taken by A to run xm is same as that of B to run (x – 120) m.

 x 11s
=
 x - 120 8s

3x = 11 x 120

x = 440.

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32.
Two boys A and B run at 4
 1 2
and 6 km an hour, Respectively. A having 190 m start.
The course being 1 km, B wins by a distance of
• A.
60 m
• C.
45 m
• B.
65 m
• D.
75 m
• Report
Explanation :

Speeds (in m/sec) of A and B are
 9 2
x
 5 18
=
 5 4
and 6 x
 5 18
=
 5 3
, respectively

A has a start of 190 m. So A has to run 1000 – 190 = 810 m while B 1000 m.

Time taken by B to cover 1000 m =
 3 5
x 1000 = 600 sec.

In this time A covers
 5 4
x 600 = 750 m.

So B reaches the wining post while A remains 810 – 750 = 60 m behind.

B wins by 60 m.

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33.
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.
364 m
• C.
324 m
• B.
254 m
• D.
354 m
• Report
Explanation :

Clearly, if A runs 600 metres, B runs = 540 m

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

Again, when B runs 500 m. C runs = 450 m

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

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34.
X, Y and Z are the three contestants in one km race. If X can give Y a start of 50 metres and X can also give Z a start of 69 metres, how many metres start Y can give Z?
• A.
10 m
• C.
20 m
• B.
40 m
• D.
25 m
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Explanation :

Here X becomes Ist, Y becomes IInd and Z becomes IIIrd in the race.

(L - x12)x23 = L(x13 - x12)

Where,

Ist (X) gives IInd (Y) a start of x12 = 50 metres

Ist (X) gives IIIrd (Y) a start of x13 = 69 metres

IInd (Y) gives IIIrd (Z) a start of x23 = ?

 Length of race(L) = 1000 metres

(1000 - 50)x23  = 1000(69 - 50)

x23  = 20 metres.

Hence Y gives Z a start of 20 metres.

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35.
In a 100 metres race, A can beat B by 25 metres and B can beat C by 4 metres. In the same race, A can beat C by -
• A.
29 metres
• C.
28 metres
• B.
21 metres
• D.
26 metres
• Report
Explanation :

A : B = 100 : 75 and B : C = 100 : 96

A : C =
 A B
x
 B C
=
 100 75
x
 100 96
=
 100 72
= 100 : 72

So, A beats C by (100 – 72) = 28 metres

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