Q 1-In a km race A can beat B by 100 m and B can beat C by 60 m. In the same race A can beat C by

A - 144 m

B - 164 m

C - 144 m

D - 154 m

```Answer - D

Explanation

"In a km race A can beat B by 100 m

=> While A run 1000 m, B run (1000-100)=900 m

In a km race B can beat C by 60 m

=> While B runs 1000 m, C runs (1000-60) =940 m

=> While B run 1 m, C run 940/1000 m
=> While B runs 900 m, C runs (940/1000) ×900 =94×9 =846 m

i.e., while A run 1000 m, C run 846 m

Hence, A can beat C by (1000-846)= 154 m
"
```

Q 2-A can run 220 metres in 41 seconds and B in 44 seconds. By how many seconds will B win if he has 30 metres start?

A - 8 sec

B - 4 sec

C - 2.5 sc

D - 3 sec

```Answer - D

Explanation

"B has a start of 30 metre

=> A has to run 220 metre and B has to run (220-30)=190 metre

Given that A takes 41 seconds to cover this 220 metre

B takes 44 seconds to cover 220 metre

=> B takes 44/220 seconds to cover 1 metre
=> B takes (44/220) ×190 =(4/20) ×190  = 38 seconds to cover 190 metre

i.e., A beats B by (41-38)= 3 seconds
"
```

Q 3-In a 100 metres race. A runs at a speed of 2 metres per seconds. If A gives B a start of 4 metres and still beats him by 10 seconds, find the speed of B.

A - 1.6 m/sec.

B - 4 m/sec.

C - 2.6 m/sec.

D - 1 m/sec.

```Answer - A

Explanation

"Speed of A = 2 m/s

Time taken by A to run 100 m distance/speed =100/2  = 50 seconds

A gives B a start of 4 metres and still A beats him by 10 seconds

=> B runs (100-4)=96 m in (50+10)=60 seconds

Speed of B = distance/time =96/60  = 1.6 m/s
"
```

Q 4-A runs 1 3â„8 times As fast as B. If A gives B a start of 90 m and they reach the goal at the same time. The goal is at a distance of

A - 330 m

B - 440 m

C - 120 m

D - 280 m

```Answer - A

Explanation

"Speed of A : Speed of B = 11â„8: 1 = 11 : 8

Let Speed of A = 11k

and Speed of B = 8k

Let the distance to the goal = x

Time taken by A = time taken by B
⇒Distance travelled by A/Speed of A
=Distance travelled by B/Speed of B
⇒ x/11k =(x−90)/8k
⇒ x/11 =(x−90)/8
⇒ 8x =11x−990
⇒3x=990
⇒x=330

Distance to the goal = 330 metre
"
```

Q 5-X, Y and Z are the three contestants in one km race. If X can give Y a start of 52 metres and X can also give Z a start of 83 metres, how many metres start Y can give Z?

A - 33.3 m

B - 32.3 m

C - 32 m

D - 32.7 m

```Answer - D

Explanation

"While X runs 1000 metre, Y runs (1000-52)=948 metre
and Z runs (1000-83)=917 metre

i.e., when Y runs 948 metre, Z runs 917 metre

=> When Y runs 1000 metre, Z runs (917/948) ×1000  = 967.30 metre

i.e., Y can give Z (1000-967.30) = 32.7 metre
"
```

Q 6-A is 2 1⁄3 times as fast as B. If A gives B a start of 80 m, how long should the race course be so that both of them reach at the same time?

A - 170 metre

B - 150 metre

C - 140 metre

D - 160 metre

```Answer - C

Explanation

"Speed of A : Speed of B = 7⁄3 : 1 = 7 : 3

It means, in a race of 7 m, A gains (7-3)=4 metre

If A needs to gain 80 metre, race should be of 7/4 ×80 = 140 metre
"
```

Q 7-In a 100 m race,A can give B 10 m and C 28 m. In the same race B can give C

A - 20 m

B - 15 m

C - 10 m

D - 25 m

```Answer - A

Explanation

"A can give B 10 m"".
=> In a 100 m race, A will have to cover 100 m while
B will have to cover only 100-10=90 m.

Similarly, ""A can give C 28 m""
=> In a 100 m race, A will have to cover 100 m while
C will have to cover only 100-28 = 72 m.

=> When B covers 90 metre, C covers 72 m

=> when B covers 100 metre, C covers (72×100)/90 = 80 metre

i.e.,in a 100 m race, B can give C 100-80=20 metre
"
```