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Question

the houses in a row are numbered consecutively from 1 to 49. Show that there exists a value of X such that sum of numbers of houses proceeding the house numbered X is equal to sum of the numbers of houses following X.


Solution

Please read the sole carefully. Hope this help you.


Given 1,2,3,4,5,....49 consecutive numbers
x is the number such that 
sum of preceding numbers of x = sum of following numbers of x


sum of ( 1,2,3,....x-1) =
sum of [(x+1), (x+2) ,....48,49]

(x-1)/2[1+x-1] =
(49-x)/2[x+1+49]

(x-1)x=(49-x)(x+50)

x²-x=49x+2450-x²-50x

x²-x =2450-x²-x

x²+x²-x+x=2450

2x²=2450

x²=2450/2

x²=1225

x=√1225

x=35


required number is x= 35


sum of (1,2,3.....34) = sum of (36,37,....49)


 

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