NCERT Solutions Class 7 Maths Comparing Quantities Exercise 8.3

Welcome, young mathematicians! In CBSE Class 7 Maths, Chapter 8 'Comparing Quantities', Exercise 8.3 is where math meets the real commercial world. Have you ever wondered how shopkeepers calculate their profit or loss? Or how banks calculate the interest when your parents deposit or borrow money? This exercise teaches you exactly that! By mastering this section, you will learn how to convert buying and selling situations into Profit and Loss percentages, and how to compute Simple Interest when money is borrowed over a period of time. Let YoLearn AI walk you through these essential concepts step-by-step, with clear definitions, visual logic, and solved NCERT-aligned practice problems that will boost your confidence for the exams.

Understanding Profit and Loss in Real Life

Whenever we buy or sell goods, two terms are crucial: Cost Price (CP) and Selling Price (SP). Cost Price is the amount paid to purchase an item, while Selling Price is the amount at which the item is sold to a customer. If the Selling Price is greater than the Cost Price (SP > CP), a Profit is made. The formula is Profit = SP - CP. Conversely, if the Cost Price is greater than the Selling Price (CP > SP), a Loss is incurred, calculated as Loss = CP - SP. To compare these gains or losses fairly across different transactions, we express them as percentages. Remember, both Profit Percentage and Loss Percentage are always calculated on the Cost Price (CP), not the Selling Price! The formulas are:

  • Profit% = (Profit / CP) * 100
  • Loss% = (Loss / CP) * 100

Step-by-Step Guide to Calculating Simple Interest

  1. Identify the Principal (P) — This is the initial sum of money borrowed, lent, or deposited.
  2. Determine the Rate of Interest (R) — This is the percentage of the principal charged as interest per year (expressed as % per annum).
  3. Note the Time Period (T) — The duration for which the money is borrowed, usually measured in years. If given in months, divide by 12 to convert to years.
  4. Calculate Simple Interest (SI) — Use the mathematical formula: SI = (P R T) / 100.
  5. Find the Total Amount (A) — Add the interest to the principal using the formula: Amount = Principal + Simple Interest.

Pro-Tips to Avoid Silly Mistakes in Exercise 8.3

  1. Always calculate profit/loss percent on CP: Students often make the mistake of dividing profit or loss by the Selling Price. Always remember, CP is your base value!
  2. Time must be in years: If a question states that money is borrowed for 6 months, don't use T = 6! Convert it to years first: T = 6/12 = 0.5 years.
  3. Units of currency: Always write the currency symbol (like ₹) in your final answers to avoid losing half a mark in school exams.

Practice Questions with Solutions

  • Q: A shopkeeper buys a toy for ₹250 and sells it for ₹285. Find his profit or loss percentage. A: Step 1: Identify CP and SP. Here, Cost Price (CP) = ₹250 and Selling Price (SP) = ₹285. Step 2: Compare SP and CP. Since SP > CP, there is a profit. Step 3: Calculate Profit = SP - CP = 285 - 250 = ₹35. Step 4: Calculate Profit Percentage using the formula: Profit% = (Profit / CP) 100. Profit% = (35 / 250) 100 = (35 * 10) / 25 = 350 / 25 = 14%. Final answer: The shopkeeper made a profit of 14%.
  • Q: Find the simple interest and amount on ₹5,000 borrowed at a rate of 12% per annum for 3 years. A: Step 1: Identify the given values. Principal (P) = ₹5,000, Rate (R) = 12% per annum, Time (T) = 3 years. Step 2: Apply the Simple Interest formula: SI = (P R T) / 100. SI = (5000 12 3) / 100 = 50 12 3 = 600 * 3 = ₹1,800. Step 3: Calculate the total amount. Amount = Principal + Simple Interest = 5000 + 1800 = ₹6,800. Final answer: Simple Interest is ₹1,800 and the Amount is ₹6,800.
  • Q: If a table is sold for ₹1,350 at a loss of 10%, what was its cost price? A: Step 1: Let the Cost Price (CP) be ₹x. Selling Price (SP) = ₹1,350 and Loss% = 10%. Step 2: Write down the relation between SP, CP, and Loss%. SP = CP - Loss = x - (10/100)*x = 0.9x. Step 3: Set up the equation: 0.9x = 1350. Step 4: Solve for x: x = 1350 / 0.9 = 13500 / 9 = 1500. Final answer: The cost price of the table was ₹1,500.
  • Q: What rate of interest per annum will yield an interest of ₹280 on a principal sum of ₹56,000 in 2 years? A: Step 1: Identify the given terms. Principal (P) = ₹56,000, Simple Interest (SI) = ₹280, Time (T) = 2 years. We need to find Rate (R). Step 2: Rearrange the SI formula to solve for R. Since SI = (P R T) / 100, we get R = (SI 100) / (P T). Step 3: Substitute the values: R = (280 100) / (56000 2) = 28000 / 112000. Step 4: Simplify the fraction: R = 28 / 112 = 1/4 = 0.25%. Final answer: The rate of interest is 0.25% per annum.

Frequently Asked Questions

What is the key difference between Profit and Profit Percentage?

Profit is the absolute monetary gain calculated as Selling Price minus Cost Price (SP - CP). Profit Percentage is that gain expressed as a fraction of the Cost Price, multiplied by 100 to allow comparisons across different transactions.

Why is profit or loss percentage always calculated on the Cost Price?

The Cost Price represents your original investment or the base value. To determine how much value was gained or lost relative to what you originally spent, you must use the Cost Price as your baseline reference.

How do I convert months into years when calculating Simple Interest?

Since the interest rate is given per annum (yearly), time must be in years. You can convert months to years by dividing the given number of months by 12.