father of ashok is builder. he planned 12 story building in gurgaon sector 5. for this he bought a plot of 500 squares yards at the rate of 1000per yard square. the builder planned the ground floor of 5m height, first floor of 4.75 m and so on .each floor is 0.25 m less than its previous floor. uptoUp to which floor the height is 33 m.
?solve it
Answers
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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