How Does a 30% Price Increase Affect Sales to Result in a 9% Revenue Decrease?

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In summary, the value of x can be determined by setting up the equation 0.91R_0 = \left( 1-\frac{x}{100}\right) \times 1.30 R_0 and solving for x.
  • #1
kiranmayi
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when the price of a box of peanuts is increased by 30% its sales decreased by x% such that the revenue decreased by 9%.what is the value of x?
solution:
let cost price=100 ,
with an increase of 30%selling price is 130, revenue is 9% lessso he incurred a loss of 9% over the income he has to get by selling x number of articles.so...
pls help me homework to solve it.just got stuck here
 
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  • #2
Let the original price be \(\displaystyle P_0\), the original sales be \(\displaystyle X_0\) and the original revenue be \(\displaystyle R_0\).

Then \(\displaystyle R_0=X_0 P_0\). Now the price is increased to \(\displaystyle P_1=1.30 P_0\), and sales become \(\displaystyle X_1=\left(1-\frac{x}{100}\right)X_0\) and revenue \(\displaystyle R_1=0.91 R_0\).

We also have:

\(\displaystyle R_1=X_1P_1\)

Substituting in from the previous paragraph we get:

\(\displaystyle 0.91R_0 = \left( 1-\frac{x}{100}\right) X_0 \times 1.30 P_0=\left( 1-\frac{x}{100}\right) \times 1.30 R_0\)

from which you can solve for \(\displaystyle x\).
 
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Related to How Does a 30% Price Increase Affect Sales to Result in a 9% Revenue Decrease?

1. What is a sales and revenue problem?

A sales and revenue problem refers to a situation where a company or business is struggling to generate enough sales and revenue to sustain its operations and meet its financial goals. This can be caused by various factors such as low demand for products or services, ineffective marketing strategies, or a decline in the overall economy.

2. How can a sales and revenue problem be identified?

A sales and revenue problem can be identified by analyzing the company's financial statements and comparing them to previous periods or industry benchmarks. Signs of a problem may include a decrease in sales, declining profit margins, or a decrease in customer retention.

3. What are common strategies for addressing a sales and revenue problem?

Common strategies for addressing a sales and revenue problem include conducting market research to identify customer needs and preferences, revising marketing and sales strategies, exploring new markets or target audiences, and improving the quality or pricing of products or services.

4. What role does data analysis and analytics play in solving sales and revenue problems?

Data analysis and analytics play a crucial role in solving sales and revenue problems. By analyzing sales data, companies can identify trends, patterns, and areas for improvement. This information can then be used to make data-driven decisions and develop effective strategies to increase sales and revenue.

5. How long does it typically take to solve a sales and revenue problem?

The time it takes to solve a sales and revenue problem can vary depending on the specific issue and the strategies implemented. In some cases, a problem can be solved relatively quickly, while others may require more time and resources. It is important for companies to regularly monitor their sales and revenue and make adjustments as needed to address any problems that arise.

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