Races and games - Quantitative Aptitude (MCQ) questions

1)   If in a game of 80, P can give 16 points to Q and R can give 20 points to P, then in a game of 150, how many points can R give to Q?
- Published on 06 Jul 15

a. 48
b. 60
c. 54
d. 90
Answer  Explanation 

ANSWER: 60

Explanation:
When P scores 80, Q scores 64.
When R scores 80, P scores 60
Hence, when R scores 150, Q scores (60 * 64 * 150) / (80 * 80) = 90
Therefore, in a game of 150, R can give 60 points to Q.


2)   If X can run 48m and Y 42m, then in a race of 1km, X beats Y by:
- Published on 06 Jul 15

a. 140m
b. 125m
c. 100m
d. 110m
Answer  Explanation 

ANSWER: 125m

Explanation:
When X runs 48m, Y runs 42m.
Hence, when X runs 1000m, Y runs (1000 * 42) / 48 = 875m
X beats Y by 125m.


3)    If in a race of 80m, A covers the distance in 20 seconds and B in 25 seconds, then A beats B by:
- Published on 06 Jul 15

a. 20m
b. 16m
c. 11m
d. 10m
Answer  Explanation 

ANSWER: 16m

Explanation:
The difference in the timing of A and B is 5 seconds. Hence, A beats B by 5 seconds.
The distance covered by B in 5 seconds = (80 * 5) / 25 = 16m
Hence, A beats B by 16m.


4)   In a race, A beats B by 15 metres and C by 29 metres. If B and C run over the course together, B wins by 15 metres. What is the length of the course?
- Published on 15 Jun 15

a. 225m
b. 120m
c. 220m
d. 160m
Answer  Explanation 

ANSWER: 225m

Explanation:
Let X be the length of the course

according to the question,
A beats B by 15 metres and C by 29 metres

Applying this,
If A runs X metres, B runs (X-15) and C runs ( X-29) metres.

B and C together run, B runs X metres and C runs (X-15)

=> If B runs 1 metre, C runs X-15/X

=> B runs X-15 m, C runs (X-15/x) * (X-15)

APPLYING THIS,
X-29 = (X-15)(X-15) / X

Solving,

X2 -29X= X2 – 30 X + 225
X = 225

Thus, length of the course is 225 metres.


5)   For a race a distance of 224 meters can be covered by P in 28 seconds and Q in 32 seconds. By what distance does P defeat Q eventually?
- Published on 19 Oct 15

a. 26m
b. 32m
c. 24m
d. 28m
Answer  Explanation 

ANSWER: 32m

Explanation:
This is a simple speed time problem. Given conditions:

=>Speed of P= 224/28 = 8m/s

=>Speed of Q=224/32 = 7m/s

=>Difference in time taken = 4 seconds

Therefore, Distance covered by P in that time= 8m/s x 4 seconds = 32 metres


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