Races And Games - Aptitude MCQ Questions and Solutions with Explanations

21

In a kilometre race, A beats B by 100 m and B beats C by 150 m. In the same race, by how many metres does A beat C ?

A) 225 m B) 235 m C) 240 m D) 250 m

Discuss

Answer & Solution

Answer: Option B

Solution:

A : B = 1000 : 900 and
B : C = 1000 : 850
$$\eqalign{ & \therefore \frac{A}{C} = \frac{A}{B} \times \frac{B}{C} \cr & \,\,\,\,\,\,\,\, = \frac{{1000}}{{900}} \times \frac{{1000}}{{850}} \cr & \,\,\,\,\,\,\,\, = \frac{{1000}}{{765}} \cr} $$
A : C = 1000 : 765
∴ A beats C by (1000 - 765) m = 235 m

22

A and B can cover a 200 m race in 22 seconds and 25 seconds respectively. When Av finished the race, then B is at what distance from the finishing line ?

A) 24 m B) 30 m C) 48 m D) 54 m

Discuss

Answer & Solution

Answer: Option A

Solution:

Distance covered by B in 25 sec = 200 m
Distance covered by B in 22 sec
=$$\left( {\frac{{200}}{{25}} \times 22} \right)$$ m
= 176 m
∴ B was at a distance of (200 - 176) m = 24 m from the finishing line.

23

In a 1000 m race, A can beat B by 100 m. In a race of 400 m, B can beat C by 40 m. By how many metres will A beat C in a race of 500 m ?

A) 85 m B) 95 m C) 105 m D) 115 m

Discuss

Answer & Solution

Answer: Option B

Solution:

A : B = 1000 : 900,
B : C = 400 : 360 = 100 : 90 = 900 : 810
⇒ A : B : C = 1000 : 900 : 810
⇒ A : C = 1000 : 810
⇒ A : C = 500 : 405
⇒ In a 500 m race, A beats C by (500 - 405) m = 95 m

24

In a 200 m 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

Discuss

Answer & Solution

Answer: Option C

Solution:

B covers 35 m in 7 seconds.
B covers 200 m in
= $$\left( {\frac{7}{{35}} \times 200} \right)$$ sec = 40 sec
Time taken by A
= (40 - 7) sec
= 33 sec

25

In a 800 metre race, A defeated B by 15 seconds. If A's speed was 8 km/hr, the speed of B was -

A) $$\frac{{16}}{{27}}{\text{ km}}/{\text{hr}}$$ B) $$\frac{{27}}{{16}}{\text{ km}}/{\text{hr}}$$ C) $$7\frac{{17}}{{25}}{\text{ km}}/{\text{hr}}$$ D) $$8\frac{{17}}{{25}}{\text{ km}}/{\text{hr}}$$

Discuss

Answer & Solution

Answer: Option C

Solution:

A's speed
= 8 km/hr
= $$\left( {8 \times \frac{5}{{18}}} \right)$$ m/sec
= $$\frac{20}{9}$$ m/sec
Time taken by A to cover 800 m
= $$\left( {800 \times \frac{9}{{20}}} \right)$$ sec
= 360 sec
Time taken by B to cover 800 m
= (360 + 15) sec
= 375 sec
∴ Speed of B :
= $$\frac{800}{375}$$ m/sec
= $$\left( {\frac{{800}}{{375}} \times \frac{{18}}{5}} \right)$$ km/hr
= $$\frac{192}{25}$$ km/hr
= $$7\frac{17}{25}$$ km/hr

26

In a 1547 m race, Arjun reaches in 78 seconds, while Karan reaches the finish point in 91 seconds. By how much distance does Arjun beat Karan?

A) 220 m B) 221 m C) 245 m D) 231 m

Discuss

Answer & Solution

Answer: Option B

Solution:

Karan,
91 sec → 1547 m
1 sec → 17 m
78 sec → 1326 m
Arjun, 78 sec → 1547 m
Karan is defeated by Arjun by
= 1547 - 1326
= 221 m

27

In a linear race of 500 m, A can beat B by 50 m and in a race of 600 m, B can beat C by 60 m. By how many metres will A beat C in a race of 400 m?

A) 70 B) 68 C) 76 D) 72

Discuss

Answer & Solution

Answer: Option C

Solution:

28

An athlete runs 8 times around a circular field of radius 7 m in 3 minutes 40 seconds. His speed (in km/h) is:

A) $$\frac{{118}}{{25}}$$ B) $$\frac{{144}}{{25}}$$ C) $$\frac{{72}}{{25}}$$ D) $$\frac{{108}}{{25}}$$

Discuss

Answer & Solution

Answer: Option B

Solution:

$$\eqalign{ & {\text{Time}} = 3\,\min 40\sec \cr & = 3\frac{{40}}{{60}} \cr & = 3\frac{2}{3} \cr & = \frac{{11}}{3}\min \cr & {\text{Circumference of circle}} = 2\pi r \cr & = 2 \times \frac{{22}}{7} \times 7 \cr & = 44{\text{ m}} \cr & {\text{Distance}} = {\text{Speed}} \times {\text{Time}} \cr & {\text{44}} \times {\text{8}} = {\text{Speed}} \times \frac{{11}}{3} \times 60 \cr & {\text{Speed}} = \frac{{32}}{{20}} \cr & {\text{Speed}} = \frac{8}{5}\,{\text{m/s}} \cr & {\text{Speed}} = \frac{8}{5} \times \frac{{18}}{5}\,{\text{km/hr}} \cr & {\text{Speed}} = \frac{{144}}{{25}}\,{\text{km/hr}} \cr} $$

29

A and B run a 5 km race on a round course of 400 m. If their speed are in the ratio 5 : 4, the number of times, the winner passes the other is

A) 1 B) 2 C) 3 D) 5

Discuss

Answer & Solution

Answer: Option B

Solution:

Ratio of speed of A and B = 5 : 4
When A runs 500 m, B runs 400 m
A will pass B every time when the distance between them is 400 m
A will cover = $$\frac{{400}}{{\left( {500 - 400} \right)}}$$ = 2000 m to overtake B each time
Number of time = $$\frac{{5000}}{{2000}}$$ = 2.5 ≈ 2 times (because .5 time is not possible)

30

A can run 250 m in 25 sec and B in 30 sec. How many metres start can A give to B in a km race so that the race may end in a dead-heat?

A) 169.53 m B) 173.82 m C) 166.67 m D) 186.34 m

Discuss

Answer & Solution

Answer: Option C

Solution:

A → 250 m → 25 second
1000 m → 100 second
B → 2500 m → 30 second
1000 m → 120 second
B should run 20 ahead, i.e. 30
30 second → 250
20 second → $$\frac{{250 \times 20}}{{30}}$$
= 166.66
= 166.67 m