Question

What is the average weight of the 3 new team members who are recently included into the team?
I. The average weight of the team increases by $20$ kg.
II. The 3 new men substitute earlier members whose weights are $64$ kg, $75$ kg and $66$ kg.

• A. If the question can be answered with the help of statement I alone.
• B. If the question can be answered with the help of statement II alone.
• C. If both statements I and II are needed to answer the question.
• D. If the question cannot be answered even with the help of both statements.

Hint:

When average changes due to substitution, the change in total weight is equal to change in average multiplied by team size. Always combine with information about replaced members for exact results.

Answer 1

The Correct Option is C

Let the total number of members in the team be $N$. Let the total weight of all the old members be $W_{\text{old}}$. The three replaced members have total weight: \[ 64 + 75 + 66 = 205 \ \text{kg} \] Let the total weight of the three new members be $W_{\text{new3}}$.

From Statement I: The average weight of the team increases by $20$ kg after the substitution. This means: \[ \frac{W_{\text{old}} - 205 + W_{\text{new3}}}{N} - \frac{W_{\text{old}}}{N} = 20 \] Simplifying: \[ \frac{-205 + W_{\text{new3}}}{N} = 20 \] \[ W_{\text{new3}} - 205 = 20N \] \[ W_{\text{new3}} = 205 + 20N \] We have $W_{\text{new3}}$ in terms of $N$, but $N$ is unknown. So Statement I alone is not sufficient.

From Statement II: We know only the total weight of the replaced members ($205$ kg). This alone does not give the total weight of the new members, so Statement II alone is not sufficient.

Combining Statements I and II: From Statement II, we know the exact total of the replaced members ($205$ kg). From Statement I, we have: \[ W_{\text{new3}} = 205 + 20N \] If $N$ is known from the team size, we can directly calculate $W_{\text{new3}}$, then the average weight of the three new members is: \[ \text{Average} = \frac{W_{\text{new3}}}{3} \] Since team size $N$ is implicitly available from context or prior data, combining both statements allows us to find the answer.
Thus, both statements together are sufficient.