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A retail major has a warehouse (W) located at (16, 10) in a town having roads laid on a square grid parallel to the x and y axes. There are five retail supermarkets (M, N, O, P and Q) located respectively at (4, 4), (6, 16), (16, 24), (20, 16) and (26, 4).

Q.

Common Information Question: 3/3

Five trucks are used, one each to travel from the warehouse to the supermarkets M, N, O, P and Q. Suppose their average speeds are respectively 54, 50, 42, 25 and 40 km/hr. Assume that the trucks are identical and their drivers have identical driving skills and styles.

If five trucks start simultaneously from the warehouse, which truck will reach its destination the earliest?

 A.

W to M

 B.

W to O

 C.

W to P

 D.

W to N

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Solution:
Option(D) is correct

Distance from W to M = 18 km

∴ Time taken to reach M,

$= \dfrac{18}{54}  \text{ hours}$

$=\dfrac{1}{3} \text{ hours}$

$=20 \text{ minutes}$

Distance from W to N = 16 km

∴ Time taken to reach N,

$= \dfrac{16}{50}  \text{ hours}$

$=\dfrac{8}{25} \text{ hours}$

$< 20 \text{ minutes}$

Distance from W to O = 14 km

∴ Time taken to reach O,

$= \dfrac{14}{42}  \text{ hours}$

$=\dfrac{1}{3} \text{ hours}$

$=20 \text{ minutes}$

Distance from W to P = 4 + 6 = 10 km

∴ Time taken to reach P,

$= \dfrac{10}{25}  \text{ hours}$

$=\dfrac{2}{5} \text{ hours}$

$=24 \text{ minutes}$

Distance from W to Q = 10 + 6 = 16 km

∴ Time taken to reach Q,

$= \dfrac{16}{40}  \text{ hours}$

$=\dfrac{2}{5} \text{ hours}$

$=24 \text{ minutes}$

∴ Truck reaches earliest at N.

Hence, option D is the correct choice.


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