Question

On 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?

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

Answer 1

The correct option is B

$2800$

Total number of students in school = $175$

Number of absent students = $35$

Number of students present = $175-35=140$

Let the total number of sweets be$"x"$.

Originally, the number of sweets received by each student = $\frac{x}{175}$

Number of sweets received by each student because of absent students = $\frac{x}{140}$

According to the question,

$$\begin{gathered} \frac{x}{140}=\frac{x}{175}+4 \\ \frac{x}{140}-\frac{x}{175}=4 \\ \frac{175x-140x}{140\times 175}=4 \\ 35x=140\times 175\times 4 \\ x=\frac{140\times 175\times 4}{35} \\ x=4\times 175\times 4 \\ x=2800 \end{gathered}$$

Hence, the total number of sweets is $2800.$