# Moderate Time, Speed & Distance Solved QuestionAptitude Discussion

 Q. $P$ beats $Q$ by 5 seconds in a race of 1000 m and $Q$ beats $R$ by 5 metres in a race of 100 m. By how many seconds does $P$ beats $R$ in a race of 1000 m?
 ✖ A. 5 sec ✖ B. 7 sec ✖ C. 10 sec ✔ D. Cannot be determined

Solution:
Option(D) is correct

If $P$ takes $t$ seconds to run 1000 m, then $Q$ takes $(t+5)$ sec.

In $(t+5)$ sec $Q$ runs 100 m whereas $R$ runs only 950 m.

$R$ runs 1000 m in $\dfrac{1000}{950}\times (t+5)$sec

$P$ takes t seconds to cover 1000m , while $R$ takes $\left(\dfrac{20t}{19}+\dfrac{100}{95}\right)$sec

From the data given, we cannot determine $t$