Aptitude Discussion

Q. |
$P$ and $Q$ start running in opposite directions (towards each other) on a circular track starting at diametrically opposite points. They first meet after $P$ has run for 75m and then they next meet after $Q$ has run 100 m after their first meeting. Assume that both of them are running a constant speed. The length of the track (in metre) is: |

✖ A. |
70 |

✖ B. |
175 |

✔ C. |
250 |

✖ D. |
350 |

**Solution:**

Option(**C**) is correct

Both $P$ and $Q$ are traveling at a constant speed, so the ratio of the distance covered by both $P$ and $Q$ will be same.

Now, assume that the length of track be $x$.

So, for the time of 1st meet,

$P$ travels $= 75 \text{ m}$ and $Q$ travels $=x/2-75 \text{ m}$

Thus, ratio $\dfrac{P}{Q}=\dfrac{75}{x/2-75}$ ---------(1)

Now, for the time of second meet.

$Q$ travels $= 100 \text{ m}$ and $P$ travels $=x-100 \text{ m}$

Thus, ratio $\dfrac{P}{Q}=\dfrac{x-100}{100}$ --------(2)

From (1) and (2),

$\dfrac{75}{x/2-75}=\dfrac{x-100}{100}$

Upon solving, we get,

$x=\textbf{250 m}$

**Edit: **Based on the comments from **Ramesh** and **Paritosh Kumar**, final answer has been changed from option(D) to option(C). The solution has been modified too.

**Ayushi Deep Srivastava**

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**Ketaki**

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Why have we done x/2 for Q when we are finding time for first meet ? Not able to get it.

**Paritosh Kumar**

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250 has to be the answer, explanation as below :

Assume track length to be T.

For first meet A travels 75, B travels T/2 - 75.

For second meet B travels 100, A travels T-100.

Solving 75/(T/2-75)=(T-100)/100

substituting options or by solving, 250 is the solution.

Thank you Paritosh for letting me know. Changed the correct option choice and modified the solution, taking inputs from your comment.

**Ramesh**

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Ratio of the distance covered by both $P$ and $Q$ will be same

Suppose length of track is $2x$

$\dfrac{75}{(x-75)}= \dfrac{(2x-100)}{100}$

$x=125$

Length of track will be 250

**Abc**

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yeah only speeds are constant, they have mentioned.

**Pranav**

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Nothing being said abt their speeds are equal !!!!!!!

P and Q are traveling at a constant speed, so the ratio of the distance covered by both P and Q will be same.

Please can someone explain me this point , speed being constant , y the ratio of the distance covered by them always same?