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CAT Exam Model Paper 3 with solutions for free online practice

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Question : 71 of 100

Marks: +1, -0

In the given diagram, river PQ is just perpendicular to the national highway AB. At a point B, highway just turns at right angle and reaches to C. PA = 500m 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 person’s Car reach from A to C via bridge covering least possible distance. What is the minimum possible required distance from A to C including the length of bridge?

4100 m
3900 m
3000 $\sqrt{2}$ m
None of the above

Solution:

(a) Let MN be the bridge ∆APM ∼ ∆ABC

∴

\frac{AP}{PM} = \frac{AB}{BC} \Rightarrow \frac{500}{PM} = \frac{1500}{3600}

⇒ PM = 1200 = QN = BR

∴ RC = BC − BR = 2400 m

and NR = BQ = 700 m

∴ NC =

\sqrt{NR^{2} + RC^{2}} = \sqrt{(700)^{2} + (2400)^{2}}

NC = 2500

m

\text{Also} AM = \sqrt{AP^{2} + PM^{2}} = \sqrt{(500)^{2} + (1200)^{2}}

AM = 1300

m

∴ Total distance to be travelled = AM + MN + NC = 1300 + 300 + 2500 = 4100 m

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