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Question

In the given diagram, river PQ is just perpendicular to the national highway AB. At a point B highway just turns to right angle and reaches to C. PA = 500 m and BQ = 700 m and width of the uniformly wide river (i.e., PQ) is 300 m. Also BC = 3600 m. A bridge has to be constructed across the river perpendicular to its stream in such a way that a person can reach from A to C via bridge covering least possible distance. PQ is the widthness of the river, then what is the minimum possible required distance from A to C including the length of the bridge? 


 


A
4100 m
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B
3900 m
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C
30002m
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D
None of these
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Solution

The correct option is C 4100 m
Let MN be the bridge
ΔAPMΔABCAPPM=ABBC500PM=15003600PM=1200=QN=BR


RC=BCBR=2400 mand NR=BQ=700 mNC=NR2+RC2NC=2500 m
Also AM=AP2+PM2AM=1300 m
Total distance to be travelled =AM+MN+NC=1300+300+2500=4100 m
 

Quantitative Aptitude

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