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GATE Exam Questions - Engineering

Q1:

The plan of a survey plotted to a scale of 10 m to 1 cm is reduced in such a way that a line originally 10 cm long now measures 9 cm. The area of the reduced plan is measured as 81 cm2. The actual (m2) of the survey is

A 10000

B 6561

C 1000

D 656

ANS:A - 10000

Representative factor, RF = (1cm/10m) =(1/1000).
Measured area = 81cm2.
Shrinkage factor, SF = 9/10 = 0.9.
SF^2 = reduced area/actual area.
0.9^2 = 81/actual area.
Actual area = 100 cm2.
RF^2 = plan area/ground area
(1/1000)^2 = 100/ground area.
Ground area = 100 * 1000^2 cm2.
Ground area = 10000 m2.