Question

In a class of 80 students, each student got sweets that are 15% of the total number of students. How many sweets were there?
(a) 1200
(b) 850
(c) 900
(d) Cannot be determined
(e) None of these

Answer 1

Hint: We solve this problem first by finding the number of sweets that each student got.
We use the condition that each student got sweets that are 15% of the total number of students to find the number of sweets that each student got.
We use the formula that the value that \[n\%\] of \['x'\] is given as \[\dfrac{n}{100}\times x\]
Then we can calculate the number of sweets that 80 students got if we can get the number of sweets that each student got.

Complete step-by-step solution
We are given that there are 80 students.
We are given that each student got sweets that are 15% of the total number of students.
Here, we can write the above statement as that each student got sweets such that 15% of 80 because there are a total of 80 students.
Let us assume that the number of sweets that each student got as \['s'\]
We know that the formula that the value that \[n\%\] of \['x'\] is given as \[\dfrac{n}{100}\times x\]
By using the above formula to 15% of 80 students then we get the number of sweets that each student got as
\[\begin{align}
  & \Rightarrow s=\dfrac{15}{100}\times 80 \\
 & \Rightarrow s=12 \\
\end{align}\]
Now, let us assume that the total number of sweets as \[N\]
We know that if each student has \['s'\] sweets, then the total number of sweets that 80 students had is given by multiplying \['s'\] with 80.
By using the above result we get the total number of sweets as
\[\begin{align}
  & \Rightarrow N=s\times 80 \\
 & \Rightarrow N=12\times 80 \\
 & \Rightarrow N=960 \\
\end{align}\]
Therefore we can say that there are a total of 960 sweets. So, option (e) is the correct answer.

Note: Students may make mistakes in the condition that each student got sweets such that 15% of the total students.
Here this conditions given the value of number of sweets that each student got as
\[\begin{align}
  & \Rightarrow s=\dfrac{15}{100}\times 80 \\
 & \Rightarrow s=12 \\
\end{align}\]
But they misunderstand the condition as that each student got sweets that are 15% of total sweets and take the equation as
\[\Rightarrow s=\dfrac{15}{100}\times N\]
Here \['N'\] is total number of sweets
Then the total number of sweets is given as
\[\Rightarrow \left( \dfrac{15}{100}\times N \right)\times 80=N\]
Here, we cannot get the value of \['N'\] and give the answer as undetermined.
But the correct condition is that each student got sweets such as 15% of the total students.
So we get the total number of sweets as
\[\begin{align}
  & \Rightarrow N=s\times 80 \\
 & \Rightarrow N=12\times 80 \\
 & \Rightarrow N=960 \\
\end{align}\]
This is the correct answer.