# CRE 5 - Linear Race | Arithmetic - Time, Speed & Distance

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**CRE 5 - Linear Race | Arithmetic - Time, Speed & Distance**

In a 600 meters race A beats B by 30 meters or 10 seconds. A’s time over the course is (in secs):

- (a)
200

- (b)
190

- (c)
210

- (d)
180

Answer: Option B

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**Explanation** :

30 meters are covered by B in 10 seconds, hence 600 meters are covered by B in 10/30 × 600 = 200 seconds.

∴ Time taken by A = (200 – 10) = 190 seconds

Hence, option (b)

Workspace:

**CRE 5 - Linear Race | Arithmetic - Time, Speed & Distance**

A can run 40 meters while B runs 50 meters. In a km race B beats A by (in meters)?

- (a)
250

- (b)
225

- (c)
200

- (d)
125

Answer: Option C

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**Explanation** :

In 50 meters race, B beats A by 10 meters.

In a km. race B beats A by (10/50 × 1000) = 200 meters

Hence, option (c)

Workspace:

**CRE 5 - Linear Race | Arithmetic - Time, Speed & Distance**

A is $1\frac{3}{8}$ times as fast as B. if A gives B a start of 150 meters, how far must be the winning post so that the race ends in a dead heat?

- (a)
100 meters

- (b)
440 meters

- (c)
200 meters

- (d)
550 meters

Answer: Option D

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**Explanation** :

The rates of A and B are 11 : 8 i.e., In the race of 11 meters A gains 3 meters

⇒ 3 meters are gained by J in a race of 11 meters

∴ 150 are gained in 11/3 × 150 = 550 meters.

Hence, option (d).

Workspace:

**CRE 5 - Linear Race | Arithmetic - Time, Speed & Distance**

In a 200 meters race. A can beat B by 50 meters and B can beat C by 8 meters. In a 100 m race, A can beat C by:

- (a)
29 meters

- (b)
21 meters

- (c)
28 meters

- (d)
26 meters

Answer: Option C

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**Explanation** :

Ratio of speeds of A : B = 200 : 150 and B : C = 200 : 192

∴ A : C = A/B × B/C = 200/150 × 200/192 = 100 ∶ 72.

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

Hence, option (c).

Workspace:

**CRE 5 - Linear Race | Arithmetic - Time, Speed & Distance**

A runs $1\frac{3}{4}$ times as fast as B. If A gives B a start of 120 meters, how far must the winning post be in order that A and B reach it at the same time?

- (a)
210 meters

- (b)
160 meters

- (c)
280 meters

- (d)
90 meters

Answer: Option C

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**Explanation** :

Ratio of rates of A and B = 7 : 4

i.e., 3 meters are gained by A in a race of 7 meters

∴ 120 m. are gained by A in a race of (7/3 × 120) = 280 meters.

Hence, option (c).

Workspace:

**CRE 5 - Linear Race | Arithmetic - Time, Speed & Distance**

A can beat B by 62 meters and C by 36 meters in a race of 400 meters. In a race of 700 meters C will beat B by:

- (a)
45.5 meters

- (b)
50 meters

- (c)
15.5 meters

- (d)
39 meters

Answer: Option B

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**Explanation** :

Ratio of rates of A, B and C = 400 : (400 – 62) : (400-36) = 400 : 338 : 364 = 200 : 169 : 182.

i.e., C gains 13 meters in a race of 182 meters.

∴ In a race of 700 meters C will gain (13/182 × 700) = 50 meters.

Hence, option (b).

Workspace:

**CRE 5 - Linear Race | Arithmetic - Time, Speed & Distance**

A and B take part in a 200 meters race. A runs at 5 km. per hour, A gives B a start of 16 meters and still beats him by 16 seconds. Speed of B is?

- (a)
5.15 kmph

- (b)
4.14 kmph

- (c)
4.25 kmph

- (d)
4.4 kmph

Answer: Option B

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**Explanation** :

A’s speed = (5 × 5/18) meters/second = 25/18 meters/second.

Time taken by A to cover 200 meters = 200 × 18/25 = 144 seconds.

∴ B covers 184 meters in (144 + 16) = 160 seconds.

B’s speed = 184/160 × 18/5 = 4.14 km/h.

Hence, option (b).

Workspace:

**CRE 5 - Linear Race | Arithmetic - Time, Speed & Distance**

In a game of 100 points, A can give B 20 points and C 28 points. Then, B can give C how many points in the same game?

- (a)
8 points

- (b)
10 points

- (c)
14 points

- (d)
40 points

Answer: Option B

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**Explanation** :

A can give 20 points to B is same as A giving a headstart of 20 points to B, i.e., when the game begins A starts with 0 points whereas B starts with 20 points.

Hence, when A scores 100 points, B scores (100 - 20 = ) 80 points and C scores (100 - 28 = ) 72 points.

A : B : C = 100 : 80 : 72

∴ B : C = 80/72 = 10/9 = 100/90.

Thus, if B scores 100, ‘C’ scores 90

∴ B can give C 10 points.

Hence, option (b)

Workspace:

**CRE 5 - Linear Race | Arithmetic - Time, Speed & Distance**

At a game of billiards, A can give B 30 points in 120 and A can give C 10 in 30. How many points can B give C in a game of 180?

- (a)
60 points

- (b)
40 points

- (c)
20 points

- (d)
24 points

Answer: Option C

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**Explanation** :

A : B = 120 : 90 and A : C = 30 : 20

A : B : C = 120 : 90 : 80

∴ B : C = 90/80 = 180/160

So, if B scores 180, then C scores 160.

∴ B, can give C 20 points in a game of 180.

Hence, option (c).

Workspace:

**CRE 5 - Linear Race | Arithmetic - Time, Speed & Distance**

In a km race, P gives Q and R starts of 10 meters and 16 meters respectively. When P crosses the finishing line, Q is 12 meters behind him and R is 20 meters behind him. How much start can Q give R in a km race so that they finish together?

- (a)
$14\frac{154}{489}$

- (b)
$13\frac{154}{498}$

- (c)
$14\frac{145}{489}$

- (d)
$15\frac{154}{489}$

Answer: Option A

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**Explanation** :

When P completes 1000m, Q completes 1000 - 10 – 12 = 978m

When P completes 1000m, R completes 1000 - 16 – 20 = 964m

i.e., when Q completes 978 m, R completes 964m

Therefore, when Q completes 1000 meters R completes $\frac{1000\times 964}{978}=\frac{482000}{489}$ m

Therefore, the start that Q can give R is 1000 - $\frac{482000}{489}=14\frac{154}{489}$

Hence, option (a).

Workspace:

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