GATE2017 EC-1: GA-8

Question

Trucks ($10$ m long) and cars ($5$ m long) go on a single lane bridge. There must be a gap of at least $20$ m after each truck and a gap of at least $15$ m after each car. Trucks and cars travel at a speed of $36$ km/h. If cars and trucks go alternately, what is the maximum number of vehicles that can use the bridge in one hour?

• A. $1440$
• B. $1200$
• C. $720$
• D. $600$

Comments

Answer 720

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plz explain

Answer 1

Length of a truck (including required gap) $= 10 m + 20 m \implies 30 m $

Length of a car (including required gap) $=5 m+ 15 m \implies 20 m$

$\therefore$ one pair of truck and car needs $30 m + 20 m = 50 m $ length

Let $n$ be the number of repetition of one pair of truck and car in $1$ hour

Given speed $= 36$ km/hr = $36000$ m/hr

$\frac{50 m \times n}{1 \text{ hr}} = 36000 m/hr$

$\implies n=\frac{36000}{50} \implies 720 \text{ pairs of vehicles}$

Total number of vehicles $= 720 \times 2 = 1440 $ vehicles

PS: We do not need the length of the bridge to solve this question as long as the length is at least $50$ m.

Answer 2

option A will be correct....