The average weight of 15 persons is increased by 2 kg when in place of a person having weight 70 kg another new person is included. The weight of the new person is:

To solve this problem, let's first understand the given information.

We are given that the average weight of 15 persons is increased by 2 kg when a new person is included. We need to find the weight of the new person.

Let's assume the sum of the weights of the 15 persons before the new person is included is "X". Therefore, the average weight of the 15 persons before the new person is included is X/15.

We are also given that the average weight increases by 2 kg when the new person is included. So, the new average weight is (X+2)/(15+1).

Now, we can set up an equation using the given information:

(X+2)/(15+1) = X/15 + 2

Let's solve this equation to find the value of X.

Multiply through by 15(15+1):

15(X+2) = X(15+1) + 2(15)(15+1)

Simplifying:

15X + 30 = 16X + 2(15)(16)

15X + 30 = 16X + 2(240)

15X + 30 = 16X + 480

Subtract 15X from both sides:

30 = X + 480

Subtract 480 from both sides:

-450 = X

Now, we have found the sum of the weights of the 15 persons before the new person is included. We need to find the weight of the new person. Let's call it "W".

W + (-450) = 70

W = 70 + 450

W = 520

Therefore, the weight of the new person is 520 kg.

Now, let's go through each option to check if any of them matches our result.

Option A) 100 - This option is incorrect because we found the weight of the new person to be 520 kg, not 100 kg. Option B) 98 - This option is incorrect because we found the weight of the new person to be 520 kg, not 98 kg. Option C) 90 - This option is incorrect because we found the weight of the new person to be 520 kg, not 90 kg. Option D) 84 - This option is incorrect because we found the weight of the new person to be 520 kg, not 84 kg.

Therefore, the correct answer is option A) 520 kg.

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