Mathematics Class 10 - Percentage Quiz

Study Notes

Problem 1: Equation derived from percentages
- Formula: (18% of 250 + 25% of 144) of ? = 54
- Breakdown:
  - 18% of 250 = 45
  - 25% of 144 = 36
  - Total = 45 + 36 = 81
  - Therefore, 81% of ? = 54
  - Solve for ?: ? = 54 / 0.81 = 66.67 (approximately)

Problem 2: Calculate the product of two percentages
- Question: 36% of 4800 x 0.2% of 1320
- Steps:
  - 36% of 4800 = 1728
  - 0.2% of 1320 = 2.64
  - Final answer: 1728 x 2.64 = 4561.92

Problem 3: Determine percentage from given values
- Solve: ?% of 35568 = 650
- Rearranging gives: ? = (650 / 35568) x 100
- Calculated percentage:
  - ? ≈ 1.83%

Multiple choice options provided for each problem
- For the first problem, options include variables and undefined values
- Second problem results with options close to calculated value (answer c: 4561.92)
- Third problem offers options ranging from 12% to 18%, none closely representing calculated 1.83%.

Understanding how to manipulate and derive equations from percentage problems aids in solving complex calculations efficiently.
Recognizing the relationships between part, whole, and percentage is vital for quick problem-solving in mathematics.

One candidate received 55% of total valid votes in the election.
15% of the total votes were invalid.
Total votes cast in the election: 15,200.
To find valid votes:
- Invalid votes = 15% of 15,200 = 2,280.
- Valid votes = Total votes - Invalid votes = 15,200 - 2,280 = 12,920.
Votes for the first candidate (55% of valid votes) = 55% of 12,920 = 7,096.
Votes for the other candidate = Valid votes - Votes for the first candidate = 12,920 - 7,096 = 5,824.
Thus, the other candidate got 5,824 valid votes.

15% of 45% of a number equals 105.3.
To find the unknown number (let's call it x):
- 15% of 45% = 0.15 * 0.45 = 0.0675.
- Therefore, 0.0675 * x = 105.3.
- Solving for x gives x = 105.3 / 0.0675 = 1,560.
To find 24% of this number (1,560):
- 24% of 1,560 = 0.24 * 1,560 = 374.4.

Jassi answered 40% of the first 125 questions correctly.
Total number of questions: 250.
To achieve a 60% overall grade on the exam:
- Total correct answers needed = 60% of 250 = 150.
Correct answers from the first half (125 questions):
- 40% of 125 = 50.
Remaining correct answers needed from the second half:
- 150 - 50 = 100.
Percent needed from the other 125 questions:
- To find percentage: (100 / 125) * 100 = 80%.

College election valid votes: 5,824 for the other candidate.
Number calculation result for the unknown number is 1,560, and 24% of that is 374.4.
Jassi needs to answer 80% of the remaining questions correctly to achieve a 60% overall grade.