Algebra
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Q.

In a green view apartment, the houses of a row are numbered consecutively from 1 to 49. Assuming that there is a value of '$x$' such that the sum of the numbers of the houses preceding the house numbered '$x$' is equal to the sum of the numbers of the houses following it. Then, what will be the value of '$x$'?

 A.

21

 B.

30

 C.

35

 D.

42

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Solution:
Option(C) is correct

From the given information,

Sum of the first $(x-1)$ natural numbers = Sum of natural number from $(x+1)$ to 49.

\(\dfrac{x(x-1)}{2}=\dfrac{49\times 50}{2}-\dfrac{x(x+1)}{2}\)

\(2x^2=49\times 50\)

\(\Rightarrow x=7\times 5= 35\)


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