Aptitude Discussion

Q. |
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? |

✔ A. |
$D$ by 7.2 m |

✖ B. |
$A$ by 7.2 m |

✖ C. |
$A$ by 8.4 m |

✖ D. |
$D$ by 8.4 m |

**Solution:**

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.**

**Sai**

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**Vaibhav Varish**

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Sa-Speed of a in meter/minute

eq1---

400/Sb-400/Sa=5

eq2---

400/Sc-400/Sb=4

eq3--

400/Sc-400/Sd=16

adding 1&2--

400/Sc-400/Sa=9;

eq3-eq2---

400/Sa-400/Sd=7

that' s why D wins by 7 min why 7.2 (Whats wrong in my solution)..pls help

the small 'm' denotes meter not minute in the question.... you are taking as minute

**Vejayanantham TR**

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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)

please elaborate.....

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.

can we apply this method on these type of question

solution is not given properly