Question

In a quiz programme the ratio of correct answers to incorrect answers is$5:2$. If 16 incorrect answers are given then the number of correct answers given is
(A). 80
(B). 40
(C). 20
(D). 30

Answer 1

Hint: From the question, we have given that the ratio of correct answers to incorrect answers is$5:2$. And using the ratio definition, we can equate this ratio with $x:16$(say x be the correct answers given). So that on solving these two ratios by equating them, we will be able to find the value of correct answers.

Complete step-by-step answer:
Given:
In a quiz programme the ratio of correct answers to incorrect answers is$5:2$
Incorrect answers given = 16
Let the Correct answers given = x
Ratio: A ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. A ratio compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed as consequent.
There are several different ways to express a ratio. One of the most common is to write a ratio using a colon as a this-to-that comparison such as correct answers to incorrect answers. Because ratios are simple division problems, they can also be written as a fraction.
A ratio might be formatted as a part to part or part to whole comparison. A part to part comparison looks at two individual quantities within a ratio of greater than two numbers. A part to whole comparison measures the number of one against the total.
$ \Rightarrow 5:2 = x:16$
$$ \Rightarrow \dfrac{5}{2} = \dfrac{x}{{16}}$$
Apply cross multiplication
$ \Rightarrow 5 \times 16 = 2 \times x$
$ \Rightarrow \dfrac{{5 \times 16}}{2} = x$
$ \Rightarrow x = 5 \times 8$
$ \Rightarrow x = 40$
Correct answers given to the quiz programme= 40

Note: No matter how a ratio is written, it is important that it can be simplified down to the smallest whole numbers possible, just as with any fraction. This can be done by finding the greatest common factor between the numbers and dividing them accordingly.