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Chapter 23: Problem 37

A fridge has a listed price of Rs 16000 . Successive discounts of \(10 \%\) and \(20 \%\) are given on its listed price. Sales tax is then charged at \(30 \%\). Ravi bought it for \(\mathrm{Rs} \mathrm{S}\) which includes the sales tax. Find \(\mathrm{S}\). (1) 16000 (2) 15848 (3) 16168 (4) 14976

Short Answer

Expert verified
Answer: (4) 14976

Step by step solution

01

Calculate Price After First Discount

To calculate the price after the first discount, we will multiply the listed price by \(1 - \frac{10}{100} = 0.90\). This will give us the price after the first discount is applied. $$(16000) (0.90) = 16000 \times 0.9 = 14400$$ So the fridge's price after the first discount is Rs. 14,400.
02

Calculate Price After Second Discount

Now, we will calculate the price after the second discount of \(20\%\). For this, we will multiply the price after the first discount (Rs. 14,400) by \(1 - \frac{20}{100} = 0.8\). $$(14400) (0.8) = 14400 \times 0.8 = 11520$$ So the fridge's price after both discounts are applied is Rs. 11,520.
03

Calculate Price After Sales Tax

Sales tax is charged at a rate of \(30\%\). To calculate the price after sales tax, we will multiply the price after the two discounts (Rs. 11,520) by \(1 + \frac{30}{100} = 1.3\). $$(11520) (1.3) = 11520 \times 1.3 = 14976$$ So the fridge's final price, including sales tax, is Rs. 14,976.
04

Match Answer with Options

Now we need to find the option that matches the final price of Rs. 14,976. The option (4) 14976 matches our calculated value of S. Therefore, Ravi bought the fridge for Rs. 14,976. So the correct answer is: (4) 14976

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Percentage Discount Calculation
Percentage discounts are a common way prices are reduced in stores. Here we will understand how to deal with successive or multiple discounts on a product, like a fridge. The main method involves multiplying the original listed price by fractions that represent the remaining price after each discount.
  • First discount: If a discount is given, like 10%, we calculate the remaining price by using the fraction \( 1 - \frac{10}{100} = 0.9 \). This means the price retains 90% of its original value.
  • Applying it to Rs 16000 leads to a new price: \( 16000 \times 0.9 = 14400 \).
  • Second discount: A subsequent 20% discount is calculated in a similar manner, \( 1 - \frac{20}{100} = 0.8 \).
  • This further reduces the price, making the cost \( 14400 \times 0.8 = 11520 \).
Keep in mind, each successive discount reduces the price based on the new reduced price, not the original. This is key when dealing with multiple discounts.
Sales Tax Calculation
Sales tax is typically a percentage added to the price of an item after any discounts have been applied. In this case, once our fridge has been reduced to Rs. 11520, we need to add sales tax.
  • A 30% sales tax would mean that for every value of 100, an additional 30 is added, calculated through the factor \( 1 + \frac{30}{100} = 1.3 \).
  • To find the price including tax, we multiply the discounted price by this factor: \( 11520 \times 1.3 = 14976 \).
Sales tax can alter the total cost significantly, so it鈥檚 vital not to forget this step during financial planning or solving word problems.
Word Problems in Mathematics
Word problems require translating a real-world situation into mathematical expressions and calculations. They can be challenging, as they involve understanding and applying multiple math skills sequentially.
  • Read the problem carefully. Note keywords like "discount," "sales tax," and the respective percentages.
  • Break down the problem into steps: First apply the discounts, then the sales tax.
  • Always verify your result against the question options to ensure your solution matches one of the choices.
  • It's helpful to write each calculation step, as word problems often combine different math concepts.
The ability to methodically solve word problems represents a deep understanding of mathematical relations, crucial for students learning mathematics.

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Most popular questions from this chapter

Amrit Raj bought a Nokia mobile for Rs 5040 which includes \(10 \%\) discount on the market price and \(12 \%\) sales tax on the remaining price. Find the marked price of the mobile phone. (1) \(\mathrm{Rs} 4672\) (2) \(\operatorname{Rs} 5124\) (3) \(\mathrm{Rs} 5000\) (4) Rs 4830

Govind earned an annual salary of Rs 330000. His employer deducted Rs 3000 per month from his salary for the first 11 months of the financial year. Find the amount of tax he paid (in \(\mathrm{Rs}\) ) in the last month of that year using the information below. If the standard deduction is \(45 \%\) of the salary or Rs 150000 , which ever is less. The income tax on the TI (taxable income) is calculated in the following manner. (i) Less than or equal to Rs \(50000-\) Nil (ii) From Rs 50000 to Rs \(100000: 20 \%\) of the amount exceeding Rs 50000 (iii) From Rs 100001 to Rs 150000 : Rs \(10,000+30 \%\) of the amount exceeding Rs 100000 (iv) Above Rs 150000: Rs \(25000+40 \%\) of the amount exceeding Rs 150000 (1) 6400 (2) 5600 (3) 4800 (4) 4600

Satish earns an annual salary of Rs 150000 and the standard deduction applicable to him is \(40 \%\) of the salary or Rs 30000, whichever is less. Then his net taxable income is (1) Rs 30000 (2) Rs 120000 (3) \(\mathrm{Rs} 60000\) (4) \(\mathrm{Rs} 90000\)

Raju purchased a car for Rs 155750 , inclusive of sales tax. He paid \(\mathrm{Rs} 5750\) as sales tax. What is the rate of sales tax? (1) \(3 \frac{2}{3} \%\) (2) \(3 \frac{3}{4} \%\) (3) \(3 \frac{4}{5} \%\) (4) \(3 \frac{5}{6} \%\)

Eswar earned an annual salary of Rs 102000 . The standard deduction was Rs 30000 . Donations upto \(10 \%\) of the gross salary were exempt from tax. He donated Rs 1050 per month to the NDF (National Defence Fund). Find his net taxable income (in \(\mathrm{Rs}\) ). (1) 59400 (2) 61800 (3) 60200 (4) 60800
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