Practice MCQ Questions and Answer on Races and Games
1.
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
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
2.
In a 100 m race, A beats B by 10 m and C by 13 m. In a race of 180 m, B will beat C by:
(A) 5.4 m
(B) 4.5 m
(C) 5 m
(D) 6 m
Solution:
$$\eqalign{ & A:B = 100:90 \cr & A:C = 100:87 \cr & \frac{B}{C} = \frac{B}{A} \times \frac{A}{C} \cr & \,\,\,\,\,\,\,\, = \frac{{90}}{{100}} \times \frac{{100}}{{87}} \cr & \,\,\,\,\,\,\,\, = \frac{{30}}{{29}} \cr} $$ When B runs180m, C runs $$ \left( {\frac{{29}}{{30}} \times 180} \right){\text{m}} = 174{\text{m}}$$ ∴ B beats C by (180 - 174) m = 6 m
3.
In a 400 metre race, A runs at a speed of 16 m/sec. If A gives B a start of 15 metres and still beats him by 10 sec, then what is the speed of B?
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
Solution:
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
5.
In a 200 metres 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
Solution:
B runs 35m in 7sec ∴ B covers 200m in $$ {\frac{7}{{35}} \times 200} = 40\sec $$ B's time over the course = 40 sec ∴ A's time over the course (40 - 7) sec = 33 sec
6.
Geeta runs times as fast as Babita. In a race, if Geeta gives a lead of 40 m to Babita, find the distance from the starting point where both of them will meet (correct up to two decimal places).