Question

The average weight of Abhi and Deeru is 40 kg. What is the average weight of Abhi, Banu, Chaitu and Deeru?
Statement 1: Average weight of Abhi, Banu and Chaitu is 45 kg
Statement 2: Average weight of Banu, Chaitu and Deeru is 40 kg

• A. statement (1) alone is sufficient to answer the question
• B. statement (2) alone is sufficient to answer the question
• C. both the statements together are needed to answer the question
• D. statement (1) alone or statement (2) alone is sufficient to answer the question
• E. neither statement (1) nor statement (2) suffices to answer the question

Answer 1

The Correct Option is C

To determine the average weight of Abhi, Banu, Chaitu, and Deeru using the given statements, let's analyze the problem step by step:

Given Data:

• The average weight of Abhi and Deeru is 40 kg.

Statement 1: Average weight of Abhi, Banu, and Chaitu is 45 kg.

Let the weights of Abhi, Banu, and Chaitu be \( A \), \( B \), and \( C \) respectively. Then the average weight can be represented as:

\(\frac{A + B + C}{3} = 45\)

Thus, the total weight of Abhi, Banu, and Chaitu is: 

\(A + B + C = 135\)

Statement 2: Average weight of Banu, Chaitu, and Deeru is 40 kg.

Let the weight of Deeru be \( D \). Then the average weight can be represented as:

\(\frac{B + C + D}{3} = 40\)

Thus, the total weight of Banu, Chaitu, and Deeru is:

\(B + C + D = 120\)

We also know from the given data that:

• The average weight of Abhi and Deeru is 40 kg, i.e., \(\frac{A + D}{2} = 40\).

This implies:

\(A + D = 80\)

Using Statements Together:

We have the following equations:

1. \(A + B + C = 135\)
2. \(B + C + D = 120\)
3. \(A + D = 80\)

We can find the value of \( A + B + C + D \) by combining these equations:

Adding equation (1) and equation (2):

\(A + B + C + B + C + D = 135 + 120\)

\(A + 2B + 2C + D = 255\)

Subtracting equation (3) from the combined equation:

\(A + 2B + 2C + D - (A + D) = 255 - 80\)

\(2B + 2C = 175\)

\(B + C = 87.5\)

Substituting \( B + C \) into equation (1):

\(A + 87.5 = 135\)

\(A = 47.5\)

Substituting \( A \) into equation (3):

\(47.5 + D = 80\)

\(D = 32.5\)

Now, we can find the average weight of Abhi, Banu, Chaitu, and Deeru:

\(A + B + C + D = 47.5 + 87.5 + 32.5\)

\(= 167.5\)

The average weight is:

\(\frac{167.5}{4} = 41.875\text{ kg}\)

Conclusion: Both statements are required to find the average weight of all four people. Thus, the correct answer is: both the statements together are needed to answer the question.