Question

The house number in Raja Karorimal lane starts with natural numbers, i.e. 1,2,3….. Sum of all the house numbers on the left side of Raja's residence in that lane is equal to the sum of all the house on its right side. There are more but less than 3000 houses on the right side of Raja's residence. Q. What is my house number?

Answer 1

Answer:

Suppose there are n houses in the left side and the total number of houses in the lane is m. Then Raja's house will be (n+1). Now n(n+1)/2= m(m+1)/2- (n+1)(n+2)/2 (n+1)2 = m(m+1)/2 There are many pairs of n and m that satisfy the equation, but n=6929 and m= 9801 is the only pair from which we shall get more than 100 but less than 3000 houses on the right side of Raja's house. So answer is (b) option.

Step-by-step explanation:

Answer 2

The correct question: The house number in Raja Karorimal lane starts with natural numbers, i.e. 1,2,3….. Sum of all the house numbers on the left side of Raja's residence in that lane is equal to the sum of all the house on its right side. There are more than 100 but less than 3000 houses on the right side of Raja's residence.

Q. What is my house number?

(a). 204

(b). 6929

(c). 288

(d). 7014.

The correct answer is option (b). 6929.

Given:

Sum of all the house numbers on the left side of Raja's residence in that lane = Sum of all the house on its right side.

Number of houses on the right side of Raja's residence < 3000.

To Find:

We have to find Raja's house number.

Solution:

Let the number of houses in the left side be n and the total number of houses in the lane be m.

Then, house number of Raja = (n+1).

Consider the equation,

$\frac{n(n+1)}{2} = \frac{m(m+1)}{2} - \frac{(n+1)(n+2)}{2 (n+1)^2 } = \frac{m(m+1)}{2}.$

Substitute the given four options in the place of n.

When n = 6929, we get m = 9801.

This is the only pair from which we will receive more than 100 but fewer than 3000 houses on the right side of Raja's house.  

So option (b). 6929 is the correct answer.

Hence, the house number of Raja is 6929.

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