On teacher's day sweets were to be equally distributed amongst 540 children. But on that particular day 135 children remained absent, hence each child got 2 sweets extra. How many sweets was each child originally supposed to get ?

Options

A. 4
B. 8
C. 10
D. 6

Answer

To solve the problem step by step, we will define the variables and set up the equations based on the information given in the question.

### Step 1: Define the variables
Let \( x \) be the number of sweets each child was originally supposed to get.

### Step 2: Calculate the total number of sweets
The total number of sweets distributed to all children is given by:
\[ \text{Total sweets} = 540 \times x \]

### Step 3: Determine the number of children present
Since 135 children were absent, the number of children present is:
\[ \text{Children present} = 540 - 135 = 405 \]

### Step 4: Calculate the sweets received by present children
Each of the 405 children who were present received \( x + 2 \) sweets. Therefore, the total number of sweets distributed to the present children is:
\[ \text{Total sweets for present children} = 405 \times (x + 2) \]

### Step 5: Set up the equation
Since the total number of sweets remains the same, we can equate the two expressions for total sweets:
\[ 540x = 405(x + 2) \]

### Step 6: Expand and simplify the equation
Expanding the right-hand side:
\[ 540x = 405x + 810 \]

### Step 7: Rearrange the equation
Now, we will move all terms involving \( x \) to one side:
\[ 540x - 405x = 810 \]
\[ 135x = 810 \]

### Step 8: Solve for \( x \)
Now, divide both sides by 135 to find \( x \):
\[ x = \frac{810}{135} = 6 \]

### Conclusion
Thus, each child was originally supposed to get **6 sweets**.

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