100+ Races and Games Aptitude Problems with Solutions - 1

Question: 1

In a 200 m race, A beats B by 35 m or 7 seconds, A’s time over the course is

(A) 33 sec

(B) 38 sec

(C) 43 sec

(D) 60 sec

Ans: A

B covers 35 m in 7 seconds.

B covers 200 m in $$({7}/{35} × 200)$$sec = 40 sec.

Time taken by A = (40 – 7)sec = 33 sec.

Question: 2

A can run 1 km in 3 mi 10 sec and B can cover the same distance in 3 min 20 sec. By what distance can A beat B?

(A) 50 m

(B) 60 m

(C) 70 m

(D) 90 m

Ans: A

A beats B by (200 – 190) sec = 10 sec.

Distance covered by B in 10 sec. = $$({1000}/{200}× 10)$$m = 50 m.

∴ A beats B by 50 m.

Question: 3

In a 100 m race covers the whole distance in 36 seconds and B in 45 seconds. In this race, A beats B by

(A) 9 m

(B) 10 m

(C) 20 m

(D) 25 m

Ans: C

Clearly, A beats B by 9 seconds.

Distance covered by B in 9 seconds = $$({100}/{45} × 9)$$m = 20 m.

∴ A beats B by 20 m.

Question: 4

In a 200 m race, A can beat B by 31 m and C by 18 m. In a race of 350 m, C will beat B by

(A) 13 m

(B) 19.5 m

(C) 22.75 m

(D) 25 m

Ans: D

A : B = 200 : 169 and A : C = 200 : 182

⇔ $${C}/{B}$$ = $$({C}/{A} × {A}/{B})$$ = $$(182/200 × 200/190)$$ = $${182}/{169}$$.

When C covers 182 m, B covers = 169 m.

When C covers 350 m, B covers = $$({169}/{182} × 350)$$m = 325 m.

∴ C beats B by 25 m.

Question: 5

At a game of billiards, A can give B 15 points in 60 and A can give C 20 points in 60. How many points can B give C in a game of 90?

(A) 10 points

(B) 12 points

(C) 20 points

(D) 30 points

Ans: A

A : B = 60 : 45 and A : C = 60 : 40

∴ $${B}/{C}$$ = $$({B}/{A} × {A}/{C})$$ = $$({45}/{60} × {60}/{45})$$ = $${45}/{40} × {2}/{2}$$ = $${90}/{80}$$ = 90 : 80.

∴ B can give 10 points in a game of 90.

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