Quantitative Aptitude
RACES AND GAMES MCQs
Races And Games Of Skill
Total Questions : 186
| Page 17 of 19 pages
Answer: Option C. -> 28 m
$$\eqalign{
& A:B = 100:75 \cr
& B:C = 100:96 \cr
& \therefore A:C = {\frac{A}{B} \times \frac{B}{C}} \cr
& = {\frac{{100}}{{75}} \times \frac{{100}}{{96}}} \cr
& = \frac{{100}}{{72}} \cr
& 100:72 \cr
& \therefore A\,\text{beats}\,C\,by \cr
& = \left( {100 - 72} \right)m \cr
& = 28\,m \cr} $$
$$\eqalign{
& A:B = 100:75 \cr
& B:C = 100:96 \cr
& \therefore A:C = {\frac{A}{B} \times \frac{B}{C}} \cr
& = {\frac{{100}}{{75}} \times \frac{{100}}{{96}}} \cr
& = \frac{{100}}{{72}} \cr
& 100:72 \cr
& \therefore A\,\text{beats}\,C\,by \cr
& = \left( {100 - 72} \right)m \cr
& = 28\,m \cr} $$
Answer: Option B. -> 235 m
A : B = 1000 : 900 and B : C = 1000 : 850
$$\eqalign{
& \therefore \frac{A}{C} = \frac{A}{B} \times \frac{B}{C} \cr
& \,\,\,\,\,\,\,\, = \frac{{1000}}{{900}} \times \frac{{1000}}{{850}} \cr
& \,\,\,\,\,\,\,\, = \frac{{1000}}{{765}} \cr} $$
A : C = 1000 : 765
∴ A beats C by (1000 - 765) m = 235 m
A : B = 1000 : 900 and B : C = 1000 : 850
$$\eqalign{
& \therefore \frac{A}{C} = \frac{A}{B} \times \frac{B}{C} \cr
& \,\,\,\,\,\,\,\, = \frac{{1000}}{{900}} \times \frac{{1000}}{{850}} \cr
& \,\,\,\,\,\,\,\, = \frac{{1000}}{{765}} \cr} $$
A : C = 1000 : 765
∴ A beats C by (1000 - 765) m = 235 m
Answer: Option B. -> 95 m
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
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
Answer: Option A. -> 24 m
Distance covered by B in 25 sec = 200 m
Distance covered by B in 22 sec=$$\left( {\frac{{200}}{{25}} \times 22} \right)$$ m = 176 m
∴ B was at a distance of (200 - 176) m = 24 m from the finishing line.
Distance covered by B in 25 sec = 200 m
Distance covered by B in 22 sec=$$\left( {\frac{{200}}{{25}} \times 22} \right)$$ m = 176 m
∴ B was at a distance of (200 - 176) m = 24 m from the finishing line.
Answer: Option C. -> $$7\frac{{17}}{{25}}{\text{ km}}/{\text{hr}}$$
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
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
Answer: Option C. -> 33 sec
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
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
Answer: Option B. -> 25 m
$$\eqalign{
& A:B = 200:169 \cr
& A:C = 200:182 \cr
& \frac{C}{B} = {\frac{C}{A} \times \frac{A}{B}} \cr
& \,\,\,\,\,\,\,\, = {\frac{{182}}{{200}} \times \frac{{200}}{{169}}} \cr
& \,\,\,\,\,\,\,\, = 182:169 \cr} $$
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
$$\eqalign{
& A:B = 200:169 \cr
& A:C = 200:182 \cr
& \frac{C}{B} = {\frac{C}{A} \times \frac{A}{B}} \cr
& \,\,\,\,\,\,\,\, = {\frac{{182}}{{200}} \times \frac{{200}}{{169}}} \cr
& \,\,\,\,\,\,\,\, = 182:169 \cr} $$
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
Answer: Option A. -> 20 m
$$\eqalign{
& {\text{Distance covered by B in 9 sec}} \cr
& = \left( {\frac{{100}}{{45}} \times 9} \right){\text{m}} \cr
& = 20\,{\text{m}} \cr
& \therefore {\text{A beats B by 20 metres}} \cr} $$
$$\eqalign{
& {\text{Distance covered by B in 9 sec}} \cr
& = \left( {\frac{{100}}{{45}} \times 9} \right){\text{m}} \cr
& = 20\,{\text{m}} \cr
& \therefore {\text{A beats B by 20 metres}} \cr} $$
Answer: Option A. -> 100 m
$$\eqalign{
& {\text{When}}\,{\text{B}}\,\,{\text{runs}}\,{\text{25m,}}\,{\text{A}}\,{\text{runs}}\,\frac{{45}}{2}m \cr
& {\text{When}}\,{\text{B}}\,\,{\text{runs}}\,{\text{1000m,}}\,{\text{A}}\,{\text{runs}} \cr
& = \left( {\frac{{45}}{2} \times \frac{1}{{25}} \times 1000} \right)m \cr
& = 900 \,m \cr
& \therefore {\text{B}}\,{\text{beats}}\,{\text{A}}\,{\text{by}}\,{\text{100 m}} \cr} $$
$$\eqalign{
& {\text{When}}\,{\text{B}}\,\,{\text{runs}}\,{\text{25m,}}\,{\text{A}}\,{\text{runs}}\,\frac{{45}}{2}m \cr
& {\text{When}}\,{\text{B}}\,\,{\text{runs}}\,{\text{1000m,}}\,{\text{A}}\,{\text{runs}} \cr
& = \left( {\frac{{45}}{2} \times \frac{1}{{25}} \times 1000} \right)m \cr
& = 900 \,m \cr
& \therefore {\text{B}}\,{\text{beats}}\,{\text{A}}\,{\text{by}}\,{\text{100 m}} \cr} $$
Answer: Option C. -> 33 sec
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
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
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