Question

x is six times as large as y. By what percent is y less than x?
(A) \[83\dfrac{1}{3}\%\]
(B) \[16\dfrac{2}{3}\%\]
(C) \[90\%\]
(D) \[60\%\]

Answer 1

Hint: In this question, we have to find out that by what percent will y be less than x as x is six times larger than y. So the exact value of y is not given here so we will consider ‘y’ to be equal to ‘p’ and to find the value of x, we will multiply the value of x by six and after taking their difference we will find out the percentage.

Complete step by step answer:
The percentage of a number indicates a hundred parts of the given quantity. The simplest way to calculate the percentage of a number is to multiply the fraction part by a hundred. In this question, we have to calculate the percent by which y is less than x. So in the numerator, the difference between x and y will be written and in the denominator, the value of x will be written. The main criteria to find out the percentage is to compare between two quantities which are given to us. The percentage is also used to calculate the marks of the students in different subjects.
In the above question, we have to find that by what percent y will be less than x and also it is given in the question that x is six times as large as y.
So, let the value of y be p.
\[y=p\]
Then the value of x will be six times as large as y which is as shown below.
\[x=6p\]
So here we come to know that the value of x will be larger than y and we have to find by what percent is y less than x. So we will take their difference and will find out its percentage.
\[percent\text{ }by\text{ }which\text{ }y\text{ }is\text{ }less\text{ }than\text{ }x\text{=}\dfrac{x-y}{x}\times 100\]……eq(1)
We know that the value of y is p and the value of x is \[6p\]. So on putting these values in eq(1), the following results will be obtained which is as shown below.
\[percent\text{ }by\text{ }which\text{ }y\text{ }is\text{ }less\text{ }than\text{ }x\text{=}\dfrac{6p-p}{6p}\times 100\]
On solving the above equation, we get the following results.
\[\begin{align}
  & percent\text{ }by\text{ }which\text{ }y\text{ }is\text{ }less\text{ }than\text{ }x\text{=}\dfrac{5}{6}\times 100 \\
 & \Rightarrow percent\text{ }by\text{ }which\text{ }y\text{ }is\text{ }less\text{ }than\text{ }x\text{=}\dfrac{5p}{6p}\times 100 \\
 & \Rightarrow percent\text{ }by\text{ }which\text{ }y\text{ }is\text{ }less\text{ }than\text{ }x\text{=83}\dfrac{1}{3}\% \\
\end{align}\]

So, the correct answer is “Option A”.

Note:
A percentage can also be expressed as a decimal or fraction in mathematics. Percentile is the term that is used in statistics. It denotes the value below which a given percentage of the given observations falls. The twenty-fifth percentile is known as the first quartile. We can also convert fractions and decimals to percentages.