Practice MCQ Questions and Answer on Races and Games

1.

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 \[\begin{array}{*{20}{c}} {}&{{\text{Ram}}}&{}&{{\text{Shyam}}} \\ {{\text{Distance}} \to }&{1200}&:&{1000} \\ {}&{12}&:&{10} \\ {{\text{Speed}} \to }&{12}&:&{10 = 12} \end{array}\]

2.

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

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

3.

In a game of 100 points, A can give B 20 points and C 28 points. Then, B can give C:

• (A) 8 points
• (B) 10 points
• (C) 14 points
• (D) 40 points

Show Answer

 $$\eqalign{ & A:B = 100:80 \cr & A:C = 100:72 \cr & \therefore \frac{B}{C} = {\frac{B}{A} \times \frac{A}{C}} = {\frac{{80}}{{100}} \times \frac{{100}}{{72}}} \cr & = \frac{{10}}{9} = \frac{{100}}{{90}} = 100:90 \cr & \therefore {\text{B}}\,{\text{can}}\,{\text{give}}\,{\text{C}}\,{\text{10}}\,{\text{points}} \cr} $$

4.

In a 100 m race, A beats B by 20 m and B beats C by 20 m. By how much distance does A beat C.

• (A) 64 m
• (B) 24 m
• (C) 25 m
• (D) 36 m

Show Answer

 $${\text{A beat C by}} = \frac{{100}}{{25}} \times 9 = 36\,{\text{m}}$$

5.

In a 400 m race, A gives B a start of 5 seconds and beats him by 15 m. In another race of 400 m, A beats B by $$7\frac{1}{7}$$ seconds. Their respective speed are -

• (A) 6 m/sec, 7 m/sec
• (B) 5 m/sec, 7 m/sec
• (C) 8 m/sec, 7 m/sec
• (D) 9 m/sec, 7 m/sec

Show Answer

 Suppose A covers 400 m in t seconds Then, B covers 385 m in (t + 5) seconds $$\eqalign{ & \therefore {\text{ B covers 400 m in}} \cr & = \left\{ {\frac{{\left( {t + 5} \right)}}{{385}} \times 400} \right\}{\text{ sec}} \cr & = \frac{{80\left( {t + 5} \right)}}{{77}}{\text{ sec}} \cr & {\text{Also, B covers 400 m in}} \cr & = \left( {t + 7\frac{1}{7}} \right){\text{ sec}} \cr & = \frac{{\left( {7t + 50} \right)}}{7}{\text{ sec}} \cr & \therefore \frac{{80\left( {t + 5} \right)}}{{77}} = \frac{{7t + 50}}{7} \cr & \Rightarrow 80\left( {t + 5} \right) = 11\left( {7t + 50} \right) \cr & \Rightarrow \left( {80t - 77t} \right) = \left( {550 - 400} \right) \cr & \Rightarrow 3t = 150 \cr & \Rightarrow t = 50 \cr & \therefore {\text{ A's speed}} \cr & = \frac{{400}}{{50}}\,m/\sec \cr & = 8\,m/\sec \cr & \therefore {\text{B's speed}} \cr & = \frac{{385}}{{55}}\,m/\sec \cr & = 7\,m/\sec \cr} $$

6.

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

Show Answer

 $$\eqalign{ & A:B = 100:90 \cr & A:C = 100:87 \cr & \frac{B}{C} = \frac{B}{A} \times \frac{A}{C} \cr & \,\,\,\,\,\,\,\, = \frac{{90}}{{100}} \times \frac{{100}}{{87}} \cr & \,\,\,\,\,\,\,\, = \frac{{30}}{{29}} \cr} $$ 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

7.

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) $$8\frac{{17}}{{25}}{\text{ km}}/{\text{hr}}$$

Show Answer

 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

8.

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

9.

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

10.

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

Show Answer

 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