CAT Exam Model Paper 3 with solutions for free online practice

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 $√2$ m
None of the above

Validate

Solution:

(a) Let MN be the bridge ∆APM ∼ ∆ABC
∴

{\AP } /{ \PM } = { \A \B } /{ \B \C } ⇒{ 500 } /{ \P \M } = { 1500 }/ { 3600 }

⇒ PM = 1200 = QN = BR

∴ RC = BC − BR = 2400 m
and NR = BQ = 700 m
∴ NC =

√ { \N \R ^ { 2 } + R C ^ { 2 } } = √ { ( 700 ) ^ { 2 } + ( 2400 ) ^ { 2 } }

NC = 2500

m

{ { \Also } \A \M = √ { \A \P ^ { 2 } + \P \M ^ { 2 } } =√ { ( 500 ) ^ { 2 } + ( 1200 ) ^ { 2 } } }

{ \A \M = 1300

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

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