Question

in a housing socity , there are 5184 houses .the houses have been constructed in such a wy that the number of houses in a row is equal to to the number of rows of house . if the first house in particular row is alloted number 1 what will be the last house in a row . please answer fast​

Answer 1

Answer:

Let there be a value of x such that the sum of the number of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it

House H

1

,H

2

,H

3

.......H

x−1

,H

x+1

........H

49

House No. 1 2 3 .......... x -1 x + 1..............49

House number will form an A.P whose first term and the common difference is 1

Sum of n terms S=

2

n

[2a+(n−1)×d]

S

x−1

=S

49

−S

x

⇒

2

(x−1)

[2(1)+(x−1−1)1]=

2

49

[2+48]−

2

x

[2(1)+(x−1)1]

⇒

2

x−1

[2+(x−2)]=

2

49

[50]−

2

x

[2+x−1]

⇒

2

x−1

[x]=

2

49

[50]−

2

x

[x+1]

⇒

2

x

[x−1+x+1]=

2

49

[50]

⇒

2

x

[2x]=49×25

⇒x

2

=49×25

⇒x=7×5=35.

Since x is not a fraction hence the value of x satisfying the given condition exists and is equal to 35.

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