[225 m] In a flat race, A beats B by 15 metres and C by 29 metres. When B and C run over the course together

For Competitive Exams

In a flat race, A beats B by 15 metres and C by 29 metres. When B and C run over the course together, B wins by 15 metres. Find the length of the course

225 m

125 m

220 m

256 m

Explanation:

Let x be the length of the course

A beats B by 15 metres and C by 29 metres

=> When A runs x metre, B runs $\left(x-15\right)$ metre and C runs $\left(x-29\right)$ metre
When B and C run over the course together, B wins by 15 metres
=> when B runs x metre, C run $\left(x-15\right)$ metre
$\text{=> when B runs 1 metre, C run }\dfrac{x-15}{x}\text{ metre}$
$\text{=> when B runs $\left(x-15\right)$ metre, C run }\dfrac{x-15}{x} \times (x-15) = \dfrac{(x-15)^2}{x}\text{ metre}$
$\text{i.e., }(x-29) = \dfrac{(x-15)^2}{x}$
$\Rightarrow x^2 - 29x = x^2 - 30x + 225$
$\Rightarrow - 29x = - 30x + 225 $
$\Rightarrow x = 225$

Additional Questions

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Important Links

A can run a kilometre in 4 min 54 sec and B in 5 min. How many metres start can A give B in a km race so that the race may end in a dead heat?	Answer
A runs 1 $\dfrac{3}{8}$ times As fast as B. If A gives B a start of 90 m and they reach the goal at the same time. The goal is at a distance of	Answer
In a 100 m race, A runs at 6 km/hr. A gives B a start of 4 m and still beats him by 4 sec. Find the speed of B.	Answer
Two boys A and B run at 4 1⁄5 and 8 km an hour respectively. A having 150 m start and the course being 1 km, B wins by a distance of	Answer
In a race of 600 m. A can beat B by 60 m and in a race of 500 m. B can beat C by 50 m. By how many metres will A beat C in a race of 400 m?	Answer
A can run 220 metres in 41 seconds and B in 44 seconds. By how many seconds will B win if he has 30 metres start?	Answer
In a game, A can give B 20 points, A can give C 32 points and B can give C 15 points. How many points make the game?	Answer
In a game A can give B 20 points in 60 and C 18 points in 90. How many points can C give B in a game of 120?	Answer
In a km race A can beat B by 100 m and B can beat C by 60 m. In the same race A can beat C by	Answer
In a flat race, A beats B by 15 metres and C by 29 metres. When B and C run over the course together, B wins by 15 metres. Find the length of the course	Answer