Question

Out of 800 oranges, 50 are rotten. Find the percentage of good oranges.
$\begin{align}
  & A)7\dfrac{1}{4}\% \\
 & B)93\dfrac{1}{4}\% \\
 & C)93\dfrac{3}{4}\% \\
 & D)7\dfrac{3}{4}\% \\
\end{align}$

Answer 1

Hint: In this question, we have to find the percentage of good oranges. Thus, we will use the basic mathematical rules, and then we will apply the percentage formula. Thus, we will first let the number of good oranges be equal to a variable that is x. Then, we will form a linear equation and solve for x. After that, we will use the percentage formula $\left( \dfrac{part}{whole}\times 100 \right)\%$ , which is the required solution to the problem.

Complete step by step solution:
According to the question, we have to find the percentage of good oranges.
Therefore, we will use the basic mathematical rules, and then we will apply the percentage formula to get the solution.
Now, we will let the value of good oranges be equal to $x$ ------ (1)
And, the total number of oranges is equal to 800 ---- (2)
Also, the number of rotten oranges are 50 -------- (3)
therefore we get the mathematical equation from (1), (2), and (3) is
Good oranges + rotten oranges = total number of oranges
$x+50=800$
Now, we will subtract 50 on both sides in the above equation, we get
$x+50-50=800-50$
As we know, the same terms with opposite signs cancel out each other, thus we get
$x=750$ ------ (4)
Thus, the number of good oranges is 750.
Now, we will find the percentage $\left( \dfrac{part}{whole}\times 100 \right)\%$ of good oranges, we get
$\left( \dfrac{\text{number of good oranges}}{\text{total number of oranges}}\times 100 \right)\%$
$\left( \dfrac{x}{\text{total number of oranges}}\times 100 \right)\%$
Thus, we will put the value of equation (2) and equation (4) in the above formula, we get
$\left( \dfrac{750}{800}\times 100 \right)\%$ ,
On further simplification, we get
$93.75\%$

Therefore, 93.75% are good oranges among all the oranges.

Note: While solving this problem, do step-by-step calculations to avoid confusion and mathematical error. One of the alternative methods to solve this problem is you can directly find the percentage using the formula $\left( \dfrac{\text{total oranges}-\text{ rotten oranges}}{\text{total number of oranges}}\times 100 \right)\%$ , to get the required result for the problem.