Time, Speed & Distance

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$P$ 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?


5 sec


7 sec


10 sec


Cannot be determined

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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 $t$

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