Q4: What is 125% expressed as a fraction in simplest form? (a) 5/4 (b) 4/5 (c) 3/2 (d) 2/3
Solution:
Ans: (a)
125% = 125/100. Dividing both numerator and denominator by 25 gives 5/4, which is the simplest form.
Q5: Simple interest on ₹5000 at 6% per annum for 2 years is: (a) ₹500 (b) ₹600 (c) ₹700 (d) ₹800
Solution:
Ans: (b)
Using the formula SI = (P × R × T)/100, we get SI = (5000 × 6 × 2)/100 = ₹600.
Fill in the Blanks
Q1: The symbol for per cent is _____.
Solution:
Ans: %
Q2: The formula for calculating profit is _____.
Solution:
Ans: SP - CP
Q3: When converting a decimal to percentage, we multiply by _____.
Solution:
Ans: 100
Q4: Amount equals Principal plus _____.
Solution:
Ans: Interest
Q5: The term 'per cent' comes from the Latin phrase _____.
Solution:
Ans: per centum
True or False
Q1: Percentages related to improper fractions are more than 100.
Solution:
Ans: True
Improper fractions have numerators greater than denominators, so when converted to percentages they exceed 100%.
Q2: Loss is calculated as CP minus SP when CP is less than SP.
Solution:
Ans: False
Loss occurs when CP is greater than SP, not when CP is less than SP, which indicates profit.
Q3: 1% is equivalent to one hundredth.
Solution:
Ans: True
The symbol % indicates hundredths, so 1% equals 1/100 or one hundredth of the whole.
Q4: Simple interest is always calculated on the selling price.
Solution:
Ans: False
Simple interest is calculated on the principal amount borrowed, not on the selling price of any item.
Q5: All parts that form a whole add up to 100%.
Solution:
Ans: True
When all parts of a whole are combined, they total 100%, representing the complete whole.
Match the Following
Column A
Column B
1. CP <>
A. Per centum
2. The Latin phrase meaning 'for each hundred'
B. (P × R × T)/100
3. Formula for simple interest
C. Profit
4. Per annum
D. CP - SP
5. Loss formula
E. Per year
Solution:
Ans:
1 - C: When cost price is less than selling price, the difference represents profit earned on the transaction.
2 - A: The term 'per cent' originates from Latin phrase 'per centum' which translates to 'for each hundred'.
3 - B: Simple interest is calculated using formula (Principal × Rate × Time)/100 for any given period.
4 - E: The term 'per annum' means per year and is used to express annual interest rates.
5 - D: Loss is calculated by subtracting selling price from cost price when CP is greater than SP.
Short Answer Questions
Q1: Explain how to convert a fraction into a percentage.
Solution:
Ans: To convert a fraction into a percentage, multiply the fraction by 100 and then place the % symbol. For example, to convert 3/4 to percentage, multiply 3/4 by 100 to get 75%. This works because percentage means parts per hundred, so we find equivalent fraction with denominator 100.
Q2: A shopkeeper bought goods for ₹8000 and sold them for ₹9200. Calculate the profit and profit percentage.
Solution:
Ans: First, calculate profit by subtracting cost price from selling price: Profit = ₹9200 - ₹8000 = ₹1200. Then calculate profit percentage using formula (Profit/CP) × 100 = (1200/8000) × 100 = 15%. Therefore, the shopkeeper earned a profit of ₹1200 with 15% profit percentage on the transaction.
Q3: What is the difference between cost price and selling price? How do they determine profit or loss?
Solution:
Ans: Cost price is the amount paid to purchase an item, whilst selling price is the amount received when selling it. If selling price exceeds cost price, the difference is profit. If cost price exceeds selling price, the difference is loss. When both are equal, there is neither profit nor loss.
Q4: Calculate the amount to be paid if someone borrows ₹10000 at 8% per annum for 3 years.
Solution:
Ans: Using simple interest formula SI = (P × R × T)/100, we get SI = (10000 × 8 × 3)/100 = ₹2400. Amount equals principal plus interest, so Amount = ₹10000 + ₹2400 = ₹12400. Therefore, the total amount to be repaid after three years is ₹12400.
Q5: In a class of 40 students, 60% are girls. How many boys are there in the class?
Solution:
Ans: If 60% are girls, then percentage of boys is 100% - 60% = 40%. To find number of boys, calculate 40% of 40 students. This equals (40/100) × 40 = 16 boys. Alternatively, number of girls = (60/100) × 40 = 24, so boys = 40 - 24 = 16.
video lectures, Worksheet: Comparing Quantities, Free, Summary, Semester Notes, mock tests for examination, Objective type Questions, pdf , past year papers, Exam, ppt, practice quizzes, Extra Questions, Worksheet: Comparing Quantities, MCQs, study material, Previous Year Questions with Solutions, Viva Questions, Worksheet: Comparing Quantities, Important questions, Sample Paper, shortcuts and tricks;
