The average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person ?

a)
76 kg

b)
76.5 kg

c)
85 kg

d)
Data inadequate

e)
None of these

Correct answer is option 'C'. Can you explain this answer?

Question

The average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person ?

a)
76 kg
b)
76.5 kg
c)
85 kg
d)
Data inadequate
e)
None of these

Correct answer is option 'C'. Can you explain this answer?

Answer

85

Answer

Given that:

- The average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg.

To find:

- What might be the weight of the new person?

Solution:

Let the weight of the new person be x kg.

Let the sum of the weights of the 8 persons be S.

So, we have:

- Average weight of 8 persons = S/8
- Average weight of 9 persons = (S + x)/9

According to the given condition:

- (S + x)/9 - S/8 = 2.5

Simplifying the above equation, we get:

- S = 520

Substituting the value of S in the above equation, we get:

- x = 85 kg

Therefore, the weight of the new person might be 85 kg.

Hence, the correct option is (c) 85 kg.

Answer

Given:
- Average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg.

To find:
- Weight of the new person.

Solution:
Let's assume the weight of the new person as 'x' kg.

Initial total weight of 8 persons = 8 * Average weight
= 8 * (Initial total weight of 8 persons / 8)
= Initial total weight of 8 persons

New total weight of 8 persons and the new person = Initial total weight of 8 persons + Weight of new person

New average weight of 8 persons and the new person = (Initial total weight of 8 persons + Weight of new person) / 9

As per the given condition,
New average weight - Initial average weight = 2.5 kg

[(Initial total weight of 8 persons + x) / 9] - (Initial total weight of 8 persons / 8) = 2.5

Solving the above equation, we get
x = 85 kg

Therefore, the weight of the new person is 85 kg, option (c) is correct.

Answer

Given:
- Average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg.

To find:
- Weight of the new person.

Solution:
Let the weight of the new person be x kg.

Before the new person came in, the sum of weights of 8 persons = 8 × Average weight = 8 × y (let's assume the average weight to be y kg)

After the new person came in, the sum of weights of 8 persons = 8y - 65 + x kg

The new average weight = (Total weight of 9 persons) / 9 = (8y - 65 + x) / 9

Given that the average weight increased by 2.5 kg when the new person came in, we can form the following equation:

(8y - 65 + x) / 9 - y = 2.5

Simplifying the above equation, we get:

8y - 65 + x - 9y = 22.5

-x + y = 87.5

We know that the weight of the new person (x) has to be greater than the weight of the person he replaced (65 kg). Therefore, we can assume:

x = 65 + a (where a is some positive number)

Substituting x in terms of a in the above equation, we get:

-(65 + a) + y = 87.5

y - a = 87.5 + 65 = 152.5

We also know that the average weight of the 9 persons is y + 2.5. Therefore, we can write:

[(8y - 65 + x) + 2.5 × 9] / 9 = y + 2.5

Simplifying the above equation and substituting x in terms of a, we get:

y + a/9 = y + 2.5

a/9 = 2.5

a = 22.5

Therefore, x = 65 + a = 85 kg.

Hence, the weight of the new person is 85 kg (option c).

Answer

Let the weight of the new person be x kg. According to the given information, the average weight of 8 persons increases by 2.5 kg. We can use the formula for average: Average = (Sum of weights)/(Number of persons) Let the sum of weights of the 8 persons be S. Then we can write: Average weight of 8 persons = S/8 When the new person is included in place of the person weighing 65 kg, the sum of weights becomes S - 65 + x. And the new average weight becomes: Average weight of 9 persons = (S - 65 + x)/9 We are given that the new average weight is 2.5 kg more than the previous average weight. So we can write: (S - 65 + x)/9 = (S/8) + 2.5 Multiplying both sides by 72 (the LCM of 8 and 9), we get: 8(S - 65 + x) = 9S + 180 Simplifying this equation, we get: 8S - 520 + 8x = 9S + 180 Solving for x, we get: x = 76.5 kg Therefore, the weight of the new person might be 76.5 kg. The answer is (b) 76.5 kg.

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The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What is the weight of the new person?

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