Question

In a race of three horses, the first beat the second by 11 metres and the third by 90 metres. If the second beat the third by 80 metres, what was the length, in metres, of the racecourse?

• A. 880
• B. 990
• C. 770
• D. 660

Answer 1

The Correct Option is A

Consider the first, second, and third horses as A, B, and C, respectively. Let the length of the racecourse be denoted as x.
The distances covered by each horse are as follows:
A B C
x (x-11) (x-90) { from 1st condition}
x (x-80) { from 2nd condition}
Setting up the equation based on the first condition:
\(x - \frac{11}{x} = \frac{x - 90}{x - 80}\)
Simplifying the equation:
⇒ x² - 91x + 880 = x² + 90x
This simplifies further to x = 880