Civil Engineering - GATE Exam Questions - Discussion

17. 

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

Answer: Option A

Explanation:

No answer description available for this question.

Unknown said: (May 6, 2017)  
Answer is (A): 10,000.

Explanation: Given: Modified length=9 cm, actual length=10 cm, actual relative factor=1/1000, modified area= 81 cm2, actual area=?

We know, Modified area= (modified relative factor/Actual relative factor)2*Actual area.
Actual area= Modified area/[(modified relative factor/Actual relative factor)2].
Actual area= 81/[(modified relative factor/1/1000)2].
Now, Modified length = (Modified RF/actual RF)*actual length.
9 cm = (Modified RF/1/1000) * 10.
Modified RF = 1/1111.11.
Actual area = 81/[(1/1111.11/1/1000)2]=99.99 = 100 cm.
As the actual scale is 1 cm to 10 m, hence.
Actual area = 100 * 102 = 10,000 m2.

Shivaprasad Sajjan said: (Feb 20, 2019)  
The scale of the original survey = 10m to 1cm.
The line originally 10cm measures 9cm.
Shrinkage factor = 9/10 = 0.9,
Reduced plan area = 81cm2.
Reduced plan area = shrinkage factor * actual plan area.
Actual plan area = 81/(0.9)^2 = 100cm2.
Actual area of survey=100*(10)^2 = 10000mts.

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