Practice MCQ Questions and Answer on Races and Games
11.
In a kilometre race, A beats B by 30 seconds and B beats C by 15 seconds. If A beats C by 180 m, the time taken by A to run 1 kilometre, is ?
(A) 200 sec
(B) 205 sec
(C) 210 sec
(D) 250 sec
Solution:
In a km race, suppose A takes t sec, Then, B takes (t + 30) sec, and C takes (t + 45) sec 180 m is covered by C in 45 sec ∴ 1000 m is covered by C in = $$\left( {\frac{{45}}{{180}} \times 1000} \right)$$ sec = 250 sec ∴ A covers 1000 m in= (250 - 45) sec = 205 sec
12.
A can give 40 metres start to B and 70 metres to C in a race of one kilometre how many metres start can B give to C in a race of one kilometre?
(A) 30 metre
(B) metre
(C) metre
(D) 32 metre
Solution:
\[\begin{array}{*{20}{c}} {\text{A}}&{\text{B}}&{\text{C}} \\ {1000}&{960}&{930} \end{array}\] ⇒ B can give C a start of 30 meters in a 960 meters race $$\eqalign{ & \Rightarrow 960\,{\text{units}} \to 30 \cr & 1\,{\text{unit}} \to \frac{1}{{32}} \cr & 1000\,{\text{units}} \to \frac{{1000}}{{32}} = 31\frac{1}{4}{\text{ meters}} \cr} $$
13.
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
14.
In a race of 200 m, A can beat B by 31 m and C by 18 m. In a race of 350 m, C will beat B by:
(A) 22.75 m
(B) 25 m
(C) 19.5 m
(D) m
Solution:
$$\eqalign{ & A:B = 200:169 \cr & A:C = 200:182 \cr & \frac{C}{B} = {\frac{C}{A} \times \frac{A}{B}} \cr & \,\,\,\,\,\,\,\, = {\frac{{182}}{{200}} \times \frac{{200}}{{169}}} \cr & \,\,\,\,\,\,\,\, = 182:169 \cr} $$ When C covers 182 m, B covers 169 m When C covers 350 m, B covers $$\left( {\frac{{169}}{{182}} \times 350} \right){\text{m}} = 325{\text{m}}$$ ∴ C beats B by (350 - 325) m = 25 m
15.
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
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
16.
In a race of 200 m, B can give a start of 10 m to A and C can give a start of 20 m to B. The start that C can give to A in the same race is ?
(A) 27 m
(B) 29 m
(C) 30 m
(D) 25 m
Solution:
B : A = 200 : 190C : B = 200 : 180 $$\eqalign{ & = \frac{C}{A} \cr & = {\frac{C}{B} \times \frac{B}{A}} \cr & = {\frac{{200}}{{180}} \times \frac{{200}}{{190}}} \cr & = \frac{{200}}{{171}} \cr} $$ ∴ C can give to A, a start of (200 - 171) m = 29 m
17.
In a game of 100 points, A can give B 20 points and C 28 points. Then, B can give C:
A and B take part in a 100 metres race. A runs at 5 km an hour. A gives B a start of 8 metres and still beats him by 8 seconds. The speed of B is ?
(A) 4.45 km/hr
(B) 4.14 km/hr
(C) 4.15 km/hr
(D) 4.25 km/hr
Solution:
A's speed = 5 km/hr = $$\left( {5 \times \frac{5}{{18}}} \right)$$ m/sec = $$\frac{25}{18}$$ m/sec Time taken by A to cover 100 metres= $$\left( {100 \times \frac{{18}}{{25}}} \right)$$ = 72 sec Time taken by B to cover 92 metres = (72 + 8) sec = 80 sec B's speed $$\frac{92}{80}$$ m/sec = $$\left( {\frac{{92}}{{80}} \times \frac{{18}}{5}} \right)$$ km/hr = $$\frac{414}{100}$$ km/hr= 4.14 km/hr
20.
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
Solution:
Beenu, 50 sec → 400 m 1 sec → 8 m 44 sec → 44 × 8 Amit,