Read the Case study given below and attempt any 4 sub parts:
Father of Ashok is a builder. He planned a 12 story building in Gurgaon sector 5. For this, he bought a
plot of 500 square yards at the rate of Rs 1000 /yard2
. The builder planned ground floor of 5 m height,
first floor of 4.75 m and so on each floor is 0.25 m less than its previous floor.
Now Answer the following questions:
i. What is the height of the last floor?
a. 2.5 m b. 2.75 m c. 2.25 m d. 3 m
ii. Which floor no is of 3 m height?
a. 5 b. 7 c. 10 d. 9
iii. What is the total height of the building?
a. 40 m b. 43.5 m c. 40.5 m d. 44 m
iv. Up to which floor the height is 33 m?
a. 8 b. 7 c. 10 d. 9
v. Which floor no. is half in height of ground or?
a. 10 b. 9 c. 12 d. 11
Answers
Step-by-step explanation:
Given : The builder planned ground floor of 5 m height,
first floor of 4.75 m and so on each floor is 0.25 m
To Find : What is the height of the last floor
Which floor no is of 3 m height
the total height of the building
Up to which floor the height is 33 m
Which floor no. is half in height of ground
Solution:
Ground floor = 5 m
first floor = 4.75 m
a = 5 d = -0.25 m
aₙ = a + (n - 1) d
height of the last floor 12 th floor
5 + (12 - 1) (-0.25)
= 5 - 2.75
= 2.25 m
floor of 3 m height
3 = 5 + (n - 1) (-0.25)
=> n = 9
total height of the building
= (12/2)(5 + 2.25)
= 43.5 m
33 = (n/2)(2*5 + (n -1)(-0.25))
=> 66 = n(10.25 - 0.25n)
=> 264 = 41n - n²
=> n² - 41n + 264 = 0
=> (n - 33)(n - 8) = 0
=> n = 8 as n = 33 is not possible
half in height of ground = 2.5 m
floor of 2.5 m height
2.5 = 5 + (n - 1) (-0.25)
=> n = 11
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