Three runners A, B and C run a race, with runner A finishing 12m ahead of runner B and 18m ahead of runner C, in another race of same type runner B finished 8m ahead of runner C. Each runner travels the entire distance at a constant speed. Find the length of the race.

Created: 3 months ago | Updated: 3 months ago

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প্রশ্নে বলা হচ্ছে যে, একটি দৌড় প্রতিযোগিতায় A, B এবং C অংশগ্রহণ করলো। প্রতিযোগিতায় B অপেক্ষা A এগিয়ে আছে 12 মিটার এবং C এর চেয়ে A এগিয়ে আছে 18 মিটার। একই রকম অন্য একটি প্রতিযোগিতায় C এর চেয়ে B এগিয়ে আছে ৪ মিটার। প্রত্যেকেই সমবেগে দৌড় প্রতিযোগিতা সম্পন্ন করে। দূরত্ব কত ছিল?

Let, total distance is x meter

Here, A finishes x meter; B finishes (x-12); C finishes (x-18) meter.

Again, in second race

If B completes x meters

∴ C completes (x - 8) meters.

So, we can write $\frac{A}{B} = \frac{x}{x - 12} & \frac{A}{C} = \frac{x}{x - 18}$

$∴ \frac{\frac{A}{C}}{\frac{A}{B}} = \frac{\frac{x}{(x - 18)}}{\frac{x}{(x - 12)}}$

$\Rightarrow \frac{B}{C} = \frac{x}{(x - 18)} \times \frac{x - 12}{x} = \frac{x - 12}{x - 18}$

$∴ \frac{B}{C} = \frac{x - 12}{x - 18} . . . . . . . . . . . (i)$

Now, equalizing equation (i) and (ii) we get

$\frac{x - 12}{x - 18} = \frac{x}{x - 8}$

$\Rightarrow x^{2} - 18 x = x^{2} - 20 x + 96$

$\Rightarrow 2 x = 96$

$∴ x = 48$

∴ Total distance is 48 meter

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