One children's day sweets were to be equally distributed among 175 students in a school. Actually on that day 35 children were absent and therefore each child got 4 sweet extra. How many sweets were available in all for distribution?

Options

A. 2750
B. 2672
C. 2675
D. 2800

Answer

To find out how many sweets were available for distribution, we can follow these steps:

1. **Determine the number of students present**:
The total number of students is 175, and 35 students were absent.
\[ \text{Students present} = 175 - 35 = 140 \]

2. **Understand the extra sweets each student received**:
Each of the 140 students received 4 extra sweets because of the absence of 35 students.

3. **Establish the ratio of sweets per student**:
If all 175 students were present, each would have received a certain number of sweets. However, since only 140 students were present, they received more sweets. The ratio of students who would have received sweets (if all were present) to those who actually received them is:
\[ \text{Ratio of students} = 175 : 140 = 5 : 4 \]
This means that if the sweets were distributed among 175 students, each would receive a certain amount, but with only 140 students, each received more sweets.

4. **Calculate the total sweets based on the ratio**:
Let’s denote the number of sweets each student would have received if all were present as \( x \). Then, the sweets received by each student when only 140 were present would be:
\[ x + 4 \]
From the ratio, we know:
\[ \frac{x + 4}{x} = \frac{4}{5} \]

5. **Cross-multiply to solve for \( x \)**:
\[ 5(x + 4) = 4x \]
\[ 5x + 20 = 4x \]
\[ 5x - 4x = -20 \]
\[ x = -20 \]
This means that \( x = 20 \) sweets per student if all 175 were present.

6. **Calculate the total number of sweets**:
Now we can find the total number of sweets by multiplying the number of sweets each student would have received by the total number of students:
\[ \text{Total sweets} = 175 \times 20 = 3500 \]

Thus, the total number of sweets available for distribution is **3500**.