Practice MCQ Questions and Answer on Races and Games

21.

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

Show Answer

 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

22.

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

Show Answer

23.

A gives B a head-start of 10 seconds in a 1500 m race and both finish the race at the same time. What is the time taken by A (in minutes) to finish the race if speed of B is 6 m/s?

• (A) 3
• (B) 4
• (C) 8
• (D) 5

Show Answer

 B's speed = 6 m/s B's distance in 10 second = 10 × 6 = 60 m \[\begin{array}{*{20}{c}} {}&{\text{A}}&{\text{B}} \\ {{\text{Distance}} \to }&{1500}&{1440} \\ {{\text{Speed}} \to }&x&6 \\ {{\text{Time}} \to }&{240{\text{ second}}}&{4\min } \end{array}\] ∵ Time same Time of B = Time of A Time of A = 4 min

24.

Amit and Beenu can cover a 400 m race in 44 seconds and 50 seconds, respectively. When Amit finished the race, then Beenu is at what distance from the finishing line?

• (A) 48 m
• (B) 52 m
• (C) 45 m
• (D) 50 m

Show Answer

 Beenu, 50 sec → 400 m 1 sec → 8 m 44 sec → 44 × 8 Amit,

25.

In a race of 1200 m, Ram can beat Shyam by 200 m or by 20 sec. What must be the speed of Ram?

• (A) 14 m/sec
• (B) 12 m/sec
• (C) 10 m/sec
• (D) 16 m/sec

Show Answer

 Shyam's speed = $$\frac{{200}}{{20}}$$ = 100 m/sec. Time constant \[\begin{array}{*{20}{c}} {}&{{\text{Ram}}}&{}&{{\text{Shyam}}} \\ {{\text{Distance}} \to }&{1200}&:&{1000} \\ {}&{12}&:&{10} \\ {{\text{Speed}} \to }&{12}&:&{10 = 12} \end{array}\]

26.

In a kilometre race, A beats B by 30 seconds and B beats C by 15 seconds. If A beats C by 180 metres, the time taken by A to run 1 kilometre is.

• (A) 250 seconds
• (B) 205 seconds
• (C) 200 seconds
• (D) 210 seconds

Show Answer

 Let the time taken by A to cover 1 km = $$x$$ seconds Time taken by B and C = $$x$$ + 30 seconds and $$x$$ + 45 seconds $$\eqalign{ & \frac{x}{{x + 45}} = \frac{{41}}{{50}} \cr & 50x = 41x + 1845 \cr & x = 205{\text{ seconds}} \cr} $$

27.

In a 1500 m race, Anil beats Bakul by 150 m and in the same race Bakul beats Charles by 75 m. By what distance does Anil beat Charles?

• (A) 217.50 m
• (B) 200.15 m
• (C) 293.50 m
• (D) 313.75 m

Show Answer

 \[\begin{array}{*{20}{c}} {}&{{\text{Anil}}}&{}&{{\text{Bakul}}} \\ {{\text{Distance}} \to }&{1500}&{}&{1350} \\ {}&{10}&:&9 \\ {}&{{\text{Bakul}}}&{}&{{\text{Charles}}} \\ {{\text{Distance}} \to }&{1500}&{}&{1425} \\ {}&{60}&:&{57} \end{array}\] Anil beats Charles by $$\eqalign{ & = \frac{{87}}{{600}} \times 1500 \cr & = \frac{{435}}{2} \cr & = 217.50{\text{ m}} \cr} $$

28.

Four sisters Suvarna, Tara, Uma and Vibha are playing a game such that the loser doubles the money of each of the other players from her share. They played four games and each sister lost one game in alphabetical order. At the end of fourth game, each sister had Rs. 32. How much money did Suvarna start with ?

• (A) Rs. 60
• (B) Rs. 34
• (C) Rs. 66
• (D) Rs. 28

Show Answer

 End of Suvarna Tara Uma Vibha 4th Game 32 32 32 32 3rd Game 16 16 16 80 2nd Game 8 8 72 40 1st Game 4 68 36 20 OriginalMoney 62 34 18 10 Survarna starts with Rs. 66

29.

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

Show Answer

 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

30.

In a 1200 m race, bike A beats bike B by 100 m. Bike B beats bike C by 100 m in a 600 m race. If bike A beats bike C by 30 sec in a 720 m race, then what is the speed of bike C?

• (A) $$\frac{{17}}{3}{\text{ m/sec}}$$
• (B) $$\frac{{26}}{9}{\text{ m/sec}}$$
• (C) $$\frac{{17}}{9}{\text{ m/sec}}$$
• (D) $$\frac{{26}}{3}{\text{ m/sec}}$$

Show Answer

 \[\begin{array}{*{20}{c}} {\text{B}}&{\text{C}} \\ {600}&{500} \\ {600\,{\text{m}}}&{{\text{Race}}} \end{array}\] $${\text{Speed}} = \frac{{170}}{{30}} = \frac{{17}}{3}{\text{m/s}}$$