RAM and Shyam are two student of Class IX. They give equal donation to a blind school in the month of March. In April each student double their donation.
(a) compare their donation in April.
(b) which mathematical concept have been covered in this question?

Answer

To solve the problem step by step, let's break it down as follows:

### Step 1: Define the Donations in March
Let the donation made by Ram in March be denoted as \( X \) and the donation made by Shyam in March be denoted as \( Y \). According to the problem, both donations are equal. Therefore, we can write:
\[ X = Y \]

### Step 2: Determine the Donations in April
In April, both Ram and Shyam double their donations. Thus, Ram's donation in April will be:
\[ \text{Ram's donation in April} = 2X \]
And Shyam's donation in April will be:
\[ \text{Shyam's donation in April} = 2Y \]

### Step 3: Compare the Donations in April
Since we established that \( X = Y \), we can substitute \( Y \) with \( X \) in Shyam's donation:
\[ \text{Shyam's donation in April} = 2Y = 2X \]
Now we can compare their donations in April:
\[ \text{Ram's donation in April} = 2X \]
\[ \text{Shyam's donation in April} = 2X \]
Thus, we conclude that:
\[ 2X = 2Y \]
This means that both Ram and Shyam donated the same amount in April.

### Step 4: Identify the Mathematical Concept
The mathematical concept covered in this problem is the **Second Axiom of Euclid**, which states that if two things are equal, then adding the same amount to both will keep them equal. In this case, since \( X = Y \), we can say that \( 2X = 2Y \).

### Final Answers:
(a) The donations in April by Ram and Shyam are equal.
(b) The mathematical concept covered is the **Second Axiom of Euclid**.