# Civil Engineering - GATE Exam Questions - Discussion

### Discussion :: GATE Exam Questions - Section 4 (Q.No.17)

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

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.

 Mahesh Sinh said: (May 22, 2020) Good, thanks for explaining @Sajjan.