Time, Speed & Distance

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A race course is 400 m long. $A$ and $B$ run a race and $A$ wins by 5m. $B$ and $C$ run over the same course and $B$ win by 4m. $C$ and $D$ run over it and $D$ wins by 16m. If $A$ and $D$ run over it, then who would win and by how much?


$D$ by 7.2 m


$A$ by 7.2 m


$A$ by 8.4 m


$D$ by 8.4 m

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Option(A) is correct

If $A$ covers 400m, $B$ covers 395 m

If $B$ covers 400m, $C$ covers 396 m

If $D$ covers 400m, $C$ covers 384 m

Now if $B$ covers 395 m, then $C$ will cover \(\dfrac{396}{400}\times 395=391.05\)m

If $C$ covers 391.05 m, then $D$ will cover \(\dfrac{400}{384}\times 391.05 = 407.24\)

If $A$ and $D$ run over 400 m, then $D$ win by 7.2 m (approx.)

Edit: For an alternative solution, check comment by Vejayanantham TR.

(3) Comment(s)

Vejayanantham TR

A - 5m

B - 4m

D -16 m

We need to find from A -> D

A->B->C = 5+4

D -> 16m

16-9 = 7 => D wins by 7m (approx)

Manohar Tangi

please elaborate.....

Nayak Sowrabh

Since the number 16 is too small in comparison to 400 u get an approximate value to be 7.

If it was a 100meter race then u would have got the answer to be -> D wins the race by 8.5m.

This is because 16 makes a lot of difference to the number 100.

so we cannot use this methodology in all those cases.