Calculating Effective Discount Percentage for Bookstore Offer
This problem asks us to find the effective discount percentage when a customer takes advantage of a bookstore's special offer. The offer is 'Buy books worth ₹1,200 or more and get ₹200 off'. The customer in question purchased books totaling ₹1,500.
Understanding the Offer and Purchase
- Offer Condition: Purchase amount must be ₹1,200 or more.
- Offer Discount: ₹200 off the total price.
- Customer's Purchase: ₹1,500.
Determining Eligibility for the Discount
First, we check if the customer's purchase meets the condition for the discount:
- The customer spent ₹1,500.
- Since ₹1,500 is greater than or equal to ₹1,200, the customer is eligible for the ₹200 discount.
Calculating the Effective Discount Percentage
The effective discount percentage tells us what fraction of the original price the discount represents. We calculate it using the formula:
$ \text{Discount Percentage} = \left( \frac{\text{Discount Amount}}{\text{Original Price}} \right) \times 100\% $
In this scenario:
- Discount Amount: ₹200
- Original Price: ₹1,500 (the amount the customer spent before the discount)
Now, let's plug these values into the formula:
$ \text{Discount Percentage} = \left( \frac{200}{1500} \right) \times 100\% $Step 1: Simplify the fraction
The fraction $\frac{200}{1500}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor. We can start by cancelling out the zeros:
$ \frac{200}{1500} = \frac{2 \times 100}{15 \times 100} = \frac{2}{15} $Step 2: Multiply by 100%
Now, multiply the simplified fraction by 100%:
$ \text{Discount Percentage} = \frac{2}{15} \times 100\% $ $ \text{Discount Percentage} = \frac{200}{15}\% $Step 3: Convert the improper fraction to a mixed number
To express the percentage in a more standard format, we convert the improper fraction $\frac{200}{15}$ to a mixed number. We perform the division $200 \div 15$:
$ 200 \div 15 = 13 \text{ with a remainder of } 5 $
So, $\frac{200}{15}$ as a mixed number is $13\frac{5}{15}$.
Step 4: Simplify the fractional part
The fraction $\frac{5}{15}$ can be simplified further by dividing both the numerator and denominator by 5:
$ \frac{5}{15} = \frac{1}{3} $Therefore, the mixed number is $13\frac{1}{3}$.
Final Result
The effective discount percentage is $13\frac{1}{3}\%$. This means the ₹200 discount represents $13\frac{1}{3}\%$ of the ₹1,500 purchase price.
Important Questions from Percentage (Notes)
- 20% of a number is more than 20% of 620 by 210. The number is:
- Girish scored 572 marks in an examination and was 30 marks short of 28% of maximum marks. In the same examination, his friend scored 473 marks. What is the percentage of marks scored by his friend?
- Anubhav spent 14% of his income on electricity bills, 28% on rent and 18% on shopping. If $\frac{1}{4}$ th of the remaining amount is ₹5120, how much did he spend on electricity bills ?
- The total population of a town is 50,000. The number of males and females increases by 10% and 15% respectively and consequently the population of the town becomes 56,000. What was the number of males in the town?
- There is an increase of 30% in the number of people coming to a theatre after reducing the entry fee by 25% per person. How much change is expected in the total earnings?
