Question

The shopkeeper increased the price of a product by \(25 \%\) so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only \(70 \%\) of the required amount. What is the net difference in the expenditure on that product? (a) \(10 \%\) more (b) \(5 \%\) more (c) \(12.5 \%\) less (d) \(17.5 \%\) less

Short answer

a) 5% less b) 10% less c) 12.5% less d) 15% less

Step-by-step solution

Determine the initial and final prices

The initial price of the product can be represented as P (100%). After increasing the price by 25%, the final price will be P(1 + 25/100) or P(1.25).

Determine the initial and final quantities

Initially, the customer would buy 100% of their required amount, represented as Q(100%). However, due to the price increase, they can now only purchase 70% of their required amount, represented as Q(0.7).

Calculate initial and final expenditures

To find the initial and final expenditures, we need to multiply the price and quantity. The initial expenditure is P * Q, and the final expenditure is 1.25P * 0.7Q.

Calculate net difference in expenditure

The net difference in expenditure can be shown as a percentage by dividing the final expenditure by the initial expenditure and then subtracting 1 and finally multiplying by 100. Net difference = (($1.25P * 0.7Q)/(P * Q) - 1) * 100 = \((1.25 * 0.7 - 1) * 100\)

Calculate the percentage

Now calculating the percentage: Net difference = \((0.875 - 1) * 100\) Net difference = \(-0.125 * 100\) Net difference = \(-12.5\) So, the net difference in the expenditure on that product is 12.5% less, which corresponds to answer option (c).

Key concepts

Profit and Loss

When dealing with profit and loss, the fundamental idea is to understand the change between the buying and selling prices. A profit occurs when a product is sold for more than its cost price, while a loss happens if the selling price falls below the cost price. This concept is critical in making decisions about pricing strategies and sales.
In the given exercise, the shopkeeper increased the price of a product by 25%. Initially, this might seem like a straightforward strategy to increase profit. However, the increase in price affected the customer's ability to purchase as much as they initially planned. This leads to a scenario where the potential profit is directly influenced by the customer's reaction to the price increase.
Understanding profit and loss also requires grasping how the change in price affects consumer behavior, which impacts the overall sales and profitability. It's a delicate balance where increasing prices might not always lead to higher profits if it leads to a decrease in the quantity sold.

Expenditure Calculation

Calculating expenditure is about determining how much money is spent on goods and services. It's crucial to grasp how different factors impact total spending. For businesses and individuals alike, keeping track of expenses helps in budgeting and financial planning.
In the context of the given problem, the initial and final expenditures need to be calculated to determine the overall impact of the price change on the customer's spending. Initially, if the price was \(P\) and the quantity \(Q\), the expenditure would be \(P \times Q\). However, with the price raised to \(1.25P\) and the quantity reduced to only 70% of \(Q\) or \(0.7Q\), the new expenditure becomes \(1.25P \times 0.7Q\).
This calculation helps us understand the exact amount of money spent compared to what was bought before the price increase. Accurately calculating this change is essential for the customer to evaluate whether they're spending more or saving money.

Percentage Decrease

Percentage decrease is a valuable tool to measure how much a quantity has been reduced. It can be especially useful when you want to understand the scale of reduction relative to the original amount.
In the example given, the customer's expenditure decreased despite the price increase because they were buying 30% less of the product than originally planned. To find the percentage decrease, you take the final value, subtract the initial value, and divide the result by the initial value, then multiply by 100 to convert it into a percentage.
In our exercise, the percentage decrease in expenditure was calculated as follows: \(((1.25 \times 0.7) - 1) \times 100\), which comes out to \(-12.5\%\). This signifies that even though the price of an individual item increased, the overall spending decreased by 12.5% due to the reduced quantity purchased. Understanding how to calculate and interpret a percentage decrease is important for making informed financial decisions.