Question

Rohan buys a pair of shoes marked at Rs 2500 . He gets a rebate of \(8 \%\) on it. After getting the rebate, sales tax is charged at the rate of \(5 \%\). What is the amount he will have to pay for the pair of shoes? (1) \(\mathrm{Rs} 2400\) (2) Rs 2415 (3) Rs 2430 (4) Rs 2445

Short answer

Answer: Rs 2415

Step-by-step solution

Calculate the Rebate Amount

To find the rebate amount, calculate 8% of the original price, which is Rs 2500. Use the following formula: Rebate Amount = (Original Price * Rebate Percentage) / 100

Calculate the Price after Rebate

To find the price after the rebate, subtract the rebate amount from the original price: Price after Rebate = Original Price - Rebate Amount

Calculate the Sales Tax Amount

Now, we will calculate the sales tax amount based on the price after rebate. Calculate the sales tax as follows: Sales Tax Amount = (Price after Rebate * Sales Tax Percentage) / 100

Calculate the Final Amount to Pay

To find the final amount Rohan has to pay, add the price after rebate and the sales tax amount: Final Amount to Pay = Price after Rebate + Sales Tax Amount Now, let's calculate the values: Step 1: Rebate Amount = (2500 * 8) / 100 = 200 Step 2: Price after Rebate = 2500 - 200 = 2300 Step 3: Sales Tax Amount = (2300 * 5) / 100 = 115 Step 4: Final Amount to Pay = 2300 + 115 = 2415 Therefore, Rohan will have to pay Rs 2415 for the pair of shoes. The correct answer is (2) Rs 2415.

Key concepts

Rebate Calculation

When you purchase something, especially during sales or special promotions, you might receive a discount called a "rebate". In Rohan's case, he bought a pair of shoes originally priced at Rs 2500, and was offered an 8% rebate.
To calculate the rebate, follow these steps:

• First, determine what percentage of the price you’re saving. Here, it’s 8%.
• Use the formula: \[ \text{Rebate Amount} = \frac{\text{Original Price} \times \text{Rebate Percentage}}{100} \]
• Plug in the numbers: \[ \text{Rebate Amount} = \frac{2500 \times 8}{100} = 200 \]
• This means Rohan saves Rs 200 on his shoes.

After computing this, subtract the rebate from the original price to find out the price after the rebate:

• \[ \text{Price after Rebate} = 2500 - 200 = 2300 \]

This new price reflects the cost after accounting for Rohan’s 8% rebate.

Sales Tax

Once you calculate the price after the rebate, it's time to consider sales tax. This is an extra percentage added to the purchase cost, which is mandated by the government.
After Rohan’s rebate, the amount that is subject to sales tax is Rs 2300. The tax rate is 5%.
To calculate the sales tax:

• Find the tax amount using:\[ \text{Sales Tax Amount} = \frac{\text{Price after Rebate} \times \text{Sales Tax Percentage}}{100} \]
• Substitute the known values:\[ \text{Sales Tax Amount} = \frac{2300 \times 5}{100} = 115 \]

This means Rohan will have to pay an additional Rs 115 as sales tax.
The total amount Rohan ends up paying involves adding the sales tax to the price after rebate:

• \[ \text{Final Amount to Pay} = 2300 + 115 = 2415 \]

Thus, after considering taxes, Rohan pays a total of Rs 2415.

Word Problems in Mathematics

Word problems are a vital part of mathematics, bridging the gap between theoretical calculations and real-life situations. They teach us how to apply mathematical concepts to everyday scenarios, just like Rohan's shopping example.
Here are a few tips to approach word problems effectively:

• Read the problem carefully and identify the key pieces of information and the question being asked.
• Translate the words into mathematical expressions or equations. For example, Rohan’s story involved a rebate and a sales tax, both requiring percentage calculations.
• Break down the problem into steps and solve each part individually. Rohan's problem was naturally segmented into calculating the rebate first, followed by the sales tax, and finally finding the total payable amount.
• Keep track of units and ensure calculations are consistent.

By mastering these strategies, students can tackle all sorts of word problems, turning them into easier-to-understand tasks. Understanding that Rohan’s pair of shoes began with a simple monetary figure and became more complex with rebates and taxes, reflects this approach.