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Chapter Analysis
Intermediate14 pages • EnglishQuick Summary
This chapter focuses on comparing quantities through concepts like ratios, percentages, and understanding discounts. It explores simple and compound interest calculations, illustrating how each can be applied to real-world situations. The chapter also discusses the applications of interest in everyday scenarios such as population growth, depreciation, and tax calculations, ensuring students can apply mathematical reasoning to practical problems.
Key Topics
- •Ratios and Proportions
- •Percentages
- •Discounts
- •Simple Interest
- •Compound Interest
- •Population Growth
- •Depreciation
- •Tax Calculations
Learning Objectives
- ✓Understand and calculate ratios and percentages.
- ✓Apply the concepts of discounts in shopping scenarios.
- ✓Calculate simple and compound interest for financial literacy.
- ✓Evaluate real-world scenarios involving growth and depreciation rates.
- ✓Develop problem-solving skills using mathematical reasoning.
- ✓Interpret and solve problems related to sales tax and GST.
Questions in Chapter
During a sale, a shop offered a discount of 10% on the marked prices of all the items. What would a customer have to pay for a pair of jeans marked at ₹1450 and two shirts marked at ₹850 each?
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The price of a TV is ₹13,000. The sales tax charged on it is at the rate of 12%. Find the amount that Vinod will have to pay if he buys it.
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Arun bought a pair of skates at a sale where the discount given was 20%. If the amount he pays is ₹1,600, find the marked price.
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I purchased a hair-dryer for ₹5,400 including 8% VAT. Find the price before VAT was added.
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An article was purchased for ₹1239 including GST of 18%. Find the price of the article before GST was added.
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Additional Practice Questions
Calculate the compound interest on ₹10,000 for 3 years at an annual interest rate of 6%.
mediumAnswer: The compound interest can be calculated using the formula A = P(1 + R/100)^n; where A is the amount, P is the principal, R is the rate of interest, and n is the number of years. A = 10000(1 + 6/100)^3 = 10000(1.06)^3 = 10000 * 1.191016 = 11910.16. Compound Interest = A - P = 11910.16 - 10000 = 1910.16.
What is the final price of an item marked at ₹7500 with two successive discounts of 20% and 10%?
mediumAnswer: First apply the 20% discount: 20% of ₹7500 is ₹1500. New price = ₹7500 - ₹1500 = ₹6000. Next, apply the 10% discount: 10% of ₹6000 is ₹600. Final price = ₹6000 - ₹600 = ₹5400.
A population of a town is 20,000 and increases at the rate of 5% per annum. What will be its population after 2 years?
hardAnswer: New population after 2 years can be calculated using the formula: P = P0(1 + r)^t; where P0 = 20,000, r = 0.05, and t = 2. P = 20000(1 + 0.05)^2 = 20000 * 1.1025 = 22050.
A machinery is bought for ₹50,000 and depreciates by 7% annually. What will be its value after 1 year?
easyAnswer: Value after 1 year can be calculated as: Value = 50000 * (1 - 0.07) = 50000 * 0.93 = ₹46,500.
Find the rate of interest per annum if the simple interest on a sum of money doubles itself in 5 years.
mediumAnswer: If the simple interest doubles the principal, SI = P and time is 5 years, hence SI = PRT/100 => P = P * R * 5 / 100. Therefore, R = 100/5 = 20%.