Question

A certain street has between 50 and 500 houses in a row, numbered 1, 2, 3, 4, consecutively. There is a certain house on the street such that the sum of all the house numbers to the left side of it is equal to the sum of all the house numbers to its right. Find the number of this house.

Answer 1

Answer:

hope you will get the answer

Answer 2

Answer:

here both the house number and no of houses are variable and is between 50 <n<500

let the number of houses be =n ,

let the house number be =x

given the sum of all the house numbers to the left side of it is equal to the sum of all the house so

1) Sx-1= Sn-Sx

so by sum of first n natural numbers formulae we get

x/2(x-1)=n/2(n+1)-x/2(x+1)

upon solving this we get

x^2=n(n+1)/2 (their is actually a trick to solve this equation which is more lenghty but correct way to solve i have solved it and  posted the answer and  you will come aross in engenerring )

if n=1,x=1

n=8,x=6

n=49,x=35

n=288,x=204 is our required solution

hope you got the answer