Question

A customer asks for the production of \(x\) number of goods. The company produces \(y\) number of goods daily. Out of which \(z \%\) are unfit for sale. The order will be completed in : (a) \(\frac{x}{100 y(1-z)}\) days (b) \(\frac{100 y z}{x}\) days (c) \(\frac{100 x}{y(100-z)}\) days (d) \(\frac{100}{y(z-1)}\) days

Short answer

Answer: (c) \(\frac{100x}{y(100-z)}\) days

Step-by-step solution

Calculate the daily fit goods

First, we need to find the number of goods produced daily that are fit for sale. Since the company produces y goods daily and z% are unfit for sale, we can find the goods fit for sale by taking the percentage of goods that are fit for sale and multiplying it by the total daily production. Fit for sale percentage = (100 - z)% Fit goods daily = \(\frac{(100 - z)}{100} * y\)

Calculate days required to complete the order

Next, we need to find the number of days required to produce x number of fit goods. To do this, we will divide the total number of goods required by the number of fit goods produced daily. Days required = \(\frac{x}{\text{Fit goods daily}}\) Substituting the expression for fit goods daily from Step 1: Days required = \(\frac{x}{\frac{(100-z)}{100} * y} = \frac{100x}{y(100-z)}\) Now we can see that the correct answer is: (c) \(\frac{100x}{y(100-z)}\) days

Key concepts

Percentage Problems

When dealing with percentage problems, it's crucial to understand what a percentage represents. Simply put, a percentage is a way of expressing a number as a fraction of 100. It is marked by the percent symbol '%' and is widely used in various calculations such as discounts, interest rates, and probability.

For instance, if 30% of a number is mentioned, it implies 30 out of every 100 units of that number. When applied to real-world scenarios, such as production quality control, translating a percentage into an actual quantity requires us to perform multiplication or division operations. In the given problem, the unfit percentage needs to be subtracted from 100% to find the fit percentage. This percentage is then applied to the daily production quantity to ascertain the count of salable goods. Understanding how to manipulate percentages and embed them into formulas is an indispensable skill in quantitative aptitude problem-solving.

Linear Equations

Linear equations are algebraic expressions that depict a straight line when plotted on a graph. They are fundamental to various disciplines, including economics, engineering, and sciences, due to their simplicity and extensive applicability. A typical linear equation is in the form of 'ax + by = c', where 'a', 'b', and 'c' are constants, and 'x' and 'y' are variables.

In contexts such as production problems or time estimation tasks, linear equations help represent relationships between different variables in a simplified and solvable manner. The exercise provided involves forming an equation to calculate the time required to fulfill an order, based on daily production and quality rates. By recognizing the direct proportionality between produced goods and time, and inversely with the percentage of unfit goods, you can create a linear equation that, once solved, yields the answer. Linear equations are a valuable tool in quantitative aptitude, especially when variables need to be isolated and operational relationships between quantities determined.

Aptitude Test Preparation

Aptitude tests are often a significant component of academic evaluations and job application processes. They are designed to assess logical reasoning, problem-solving ability, and sometimes even personality traits. Preparation for these tests is essential and involves familiarity with a range of topics, including numeracy, verbal reasoning, and abstract thinking.

To excel in quantitative sections, such as percentage problems and linear equations, practice is key. Begin by mastering fundamental concepts and gradually progress to more complex scenarios. Use a step-by-step approach to dissect problems, ensuring a deep understanding of every stage involved in reaching the solution. It's also beneficial to time yourself while practicing, to improve speed and accuracy. Additionally, seek out practice tests and sample problems to diversify your exposure to various question types. The discipline and strategies you develop from structured aptitude test preparation will not only help you in assessments but also foster a mindset that facilitates logical reasoning in everyday life.