- LPU MCA Semester 1
- PEA515
- Unit 2
PEA515 · Unit 2: Percentage and profit and loss
Percentage problems on marks, election, population and error
30 practice questions · in the MTE and ETE syllabus
Key points
- Candidate shares are computed on valid votes
- Area error = 2x + x^2/100 percent
- Reverse a growth by dividing by its factor
- Shares of income sum to 100 percent
Marks: passing marks = pass percentage of total marks; a student who scores m and fails by f has m + f as the passing mark.
Election: valid votes = total votes - invalid votes. A candidate's share is taken on valid votes. In a two-candidate contest, margin = (winner% - loser%) of valid votes, and winner% + loser% = 100.
Population: with increases of a% then b% use successive change; to go back from the final value, divide by the growth factor.
Error: if a side of a square is measured with an x% error, the area error is 2x + x^2/100 percent. A 5% error in the side gives 10.25% in the area.
Expenditure and savings: shares of income add up to 100%; savings = income minus the listed expenses.
Exam trap: applying a percentage to total votes when the question gives it for valid votes.
Try two questions
In an exam 72% of the candidates passed in maths and 64% in science while 8% failed in both. What percent passed in both?
- 36%
- 64%
- 44%
- 136%
Show the answer
C. Passed at least one = 92%; both = 72 + 64 - 92 = 44%.
Why not A: Ignores the students who failed both.
Why not B: Takes the smaller pass percentage as the overlap.
Why not D: Adds the two pass percentages without removing the union.
At a school test, 70% cleared English and 68% cleared reasoning; 8% cleared neither. What percentage cleared both?
- 46%
- 38%
- 68%
- 138%
Show the answer
A. Passed at least one = 92%; both = 70 + 68 - 92 = 46%.
Why not B: Ignores the students who failed both.
Why not C: Takes the smaller pass percentage as the overlap.
Why not D: Adds the two pass percentages without removing the union.