Question

In a Quiz program the ratio of correct answers to incorrect answers is \[5:2\]. If \[16\] incorrect answers are given, then the number of correct answer given is
A. \[80\]
B. \[40\]
C. \[20\]
D. \[30\]

Answer 1

Hint:Here we assume the number of correct answers and number of incorrect answers as separate variables and use the concept of ratio to form an equation showing a relation between the number of correct answers and incorrect answers then we substitute the value of given number of incorrect answers in that equation in the end.

Complete step-by-step answer:
Assume the number of correct answers given in a quiz be \[x\].
Assume the number of incorrect answers given in a quiz be \[y\].
We know the ratio\[m:n\] of any number \[m\] to \[n\] can be written as \[\dfrac{m}{n}\].
We are given the ratio of number of correct answers to the number of incorrect answers as \[5:2\].
Therefore we can write the ratio \[x:y = 5:2\]
 \[\dfrac{x}{y} = \dfrac{5}{2}\] \[...(i)\]
Whenever we have an equation where there are values in the denominator on both sides, we can cross multiply the denominator of a side to the numerator of the other side to solve the equation.
Cross multiplying the values on both sides of the equation \[(i)\]
\[
  2 \times x = 5 \times y \\
  2x = 5y \\
 \] \[(ii)\]
We are given the total number of incorrect answers as \[16\]
Therefore value of \[y = 16\]
Substitute the value in equation \[(ii)\]
\[
  2x = 5 \times (16) \\
  2x = 80 \\
 \]
Now, dividing both sides of the equation by \[2\] will give us the value of \[x\]
\[\dfrac{{2x}}{2} = \dfrac{{80}}{2}\]
\[x = 40\]
Therefore, number of correct answers given in the quiz is \[40\]
So, option B is correct.

Note:Students should check that ratio should always be in the simplest from i.e. there should be no common factor between the numerator and denominator, if any cancel them out.
If we are given a ratio \[x:y = m:n\]then we can say that \[n\] times \[x\] will give us \[m\] times \[y\].