Practice | Hashtable

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

Solution:

A : B = 1000 : 900 and
B : C = 1000 : 850

\begin{aligned} ∴ \frac{A}{C} = \frac{A}{B} \times \frac{B}{C} \\ = \frac{1000}{900} \times \frac{1000}{850} \\ = \frac{1000}{765} \end{aligned}

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

Solution:

Distance covered by B in 25 sec = 200 m
Distance covered by B in 22 sec
=

(\frac{200}{25} \times 22)

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

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

Solution:

B covers 35 m in 7 seconds.
B covers 200 m in
=

(\frac{7}{35} \times 200)

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. $\frac{16}{27} km / hr$

B. $\frac{27}{16} km / hr$

C. $7 \frac{17}{25} km / hr$

D. $8 \frac{17}{25} km / hr$

Discuss

Solution:

A's speed
= 8 km/hr
=

(8 \times \frac{5}{18})

m/sec
=

\frac{20}{9}

m/sec
Time taken by A to cover 800 m
=

(800 \times \frac{9}{20})

sec
= 360 sec
Time taken by B to cover 800 m
= (360 + 15) sec
= 375 sec
∴ Speed of B :
=

\frac{800}{375}

m/sec
=

(\frac{800}{375} \times \frac{18}{5})

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

No explanation ¯\_(ツ)_/¯

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

No explanation ¯\_(ツ)_/¯

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

No explanation ¯\_(ツ)_/¯

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

No explanation ¯\_(ツ)_/¯

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

No explanation ¯\_(ツ)_/¯