The correct answer is option (C):
both the statements together are needed to answer the question
Let's analyze the problem. We're given that the average weight of Abhi and Deeru is 40 kg. We want to find the average weight of Abhi, Banu, Chaitu, and Deeru.
We can represent the given information as follows:
* (Abhi + Deeru) / 2 = 40 => Abhi + Deeru = 80 (Equation 1)
Now let's examine the statements:
Statement 1: The average weight of Abhi, Banu, and Chaitu is 45 kg.
This can be written as:
* (Abhi + Banu + Chaitu) / 3 = 45 => Abhi + Banu + Chaitu = 135 (Equation 2)
Statement 2: The average weight of Banu, Chaitu, and Deeru is 40 kg.
This can be written as:
* (Banu + Chaitu + Deeru) / 3 = 40 => Banu + Chaitu + Deeru = 120 (Equation 3)
Now consider how we can solve the question. We need (Abhi + Banu + Chaitu + Deeru) / 4.
* Using only Statement 1, we can't find Deeru. We can't determine the sum (Abhi + Banu + Chaitu + Deeru)
* Using only Statement 2, we can't find Abhi. We can't determine the sum (Abhi + Banu + Chaitu + Deeru)
However, if we use both statements together:
We have:
* Abhi + Deeru = 80 (From the problem)
* Abhi + Banu + Chaitu = 135 (Statement 1)
* Banu + Chaitu + Deeru = 120 (Statement 2)
From statement 1, we can get Banu + Chaitu = 135 - Abhi.
Substituting this in the equation given by statement 2, we get (135 - Abhi) + Deeru = 120. Therefore, Deeru - Abhi = -15.
We also know Abhi + Deeru = 80. Adding these two equations, we get 2*Deeru = 65, and Deeru = 32.5.
Hence Abhi = 47.5.
From statement 1: Banu + Chaitu = 135 - 47.5 = 87.5
Thus, Abhi + Banu + Chaitu + Deeru = 47.5 + 87.5 + 32.5 = 167.5
The average of the four would be 167.5/4 = 41.875
Therefore, to find the answer we need both the statements.