- LPU MCA Semester 1
- PEA515
- Unit 2
PEA515 · Unit 2: Percentage and profit and loss
Successive percent change
30 practice questions · in the MTE and ETE syllabus
Key points
- Net change = a + b + ab/100
- Convert each change to a multiplying factor
- A rise then an equal fall always loses x squared over 100 percent
- Consumption cut = r/(100+r) of the old amount
Changes do not add; they multiply. A rise of a% followed by a rise of b% gives a net change of a + b + ab/100 percent. Treat a fall as a negative value: +20% then -10% gives 20 - 10 - 2 = +8%.
Convert each change to a factor (1.20 for +20%, 0.90 for -10%) and multiply: 1.20 x 0.90 = 1.08, a net 8% rise.
Useful results:
- A rise of x% followed by a fall of x% leaves a loss of x^2/100 percent.
- To keep expenditure unchanged after a price rise of r%, cut consumption by r/(100 + r) x 100 percent.
- Growth over n periods: P x (1 + r/100)^n; for decay use (1 - r/100)^n.
Exam trap: adding the percentages directly or applying the second change to the original base.
Try two questions
A price is increased by 12%, then increased by 25%, then increased by 12%. What is the net percentage change overall?
- 56.8%
- 49%
- 16.33%
- -56.8%
Show the answer
A. Multiply the growth factors (28/25 x 5/4 x 28/25); net change is that product minus 1, expressed as a percentage.
Why not B: Adds the percentages directly; successive changes compound on the new base.
Why not C: Averages the changes instead of compounding them.
Why not D: Reverses the sign of the final result.
A salary is increased by 5%, then decreased by 8%. What is the net percentage change overall?
- -3%
- -2.6%
- -3.4%
- -1.5%
Show the answer
C. Multiply the growth factors (21/20 x 23/25); net change is that product minus 1, expressed as a percentage.
Why not A: Adds the percentages directly; successive changes compound on the new base.
Why not B: Applies the cross-term with the wrong sign.
Why not D: Averages the changes instead of compounding them.