Question

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Answer 1

Solution:

Sum of no. of houses preceding to the house numbered 'x'
= Sum of natural numbers from 1 to (x-1).

Also, sum of no. of houses following it
= Sum of (x+1) to 49.
or we can write as,
= (Sum of natural numbers up to 49) - (Sum of natural numbers up to x).

Since we know that sum of natural numbers up to 'n' is given by n(n+1)/2.

Then according to the given conditions we get,
(x-1) [(x-1) +1]/2 = [49(49+1)/2 - x(x+1)/2]
or (x^2 - x)/2 = [2450 - x^2 -x]/2
or 2x^2 = 2450
or x^2 = 1225
or x = √1225
Therefore, x = 35.

Hence, sum of natural numbers up to 34 should be equal to sum of natural numbers from 36 to 49.

Check,
34(34+1)/2 = 34 × 35 / 2
= 595.

and
49(49+1)/2 - 35(35+1)/2
= 49×50/2 - 35×36/2
= 1225 - 630
= 595.

Therefore, both are equal.
Hence x = 35 is the answer.