Races and games - Quantitative Aptitude (MCQ) questions for Q. 99

Q.  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: 225m
 
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.

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