Lesson 28 of 100 | Quantitative Aptitude / Percentages / प्रतिशत
Percentage increase and decrease
Learning outcome
Calculate increased or decreased quantities, recover the percentage change from two amounts, and distinguish percentage change from percentage-point change.
Keep the original base
A percentage increase or decrease compares the change with the original quantity, not the final quantity. The original is the nonzero reference; all quantities here are positive.
For an increase, change = new − original. Percentage increase = (change/original) × 100%. For a decrease, use change = original − new to obtain a positive amount of reduction, then divide by the original.
Why use the original? The question asks how large the movement is relative to where the quantity started. Dividing by the final amount answers a different comparison.
For an increase of p%, new quantity = original × (1 + p/100). The original contributes one whole, and the increase contributes p/100 of that same whole. For a decrease, new quantity = original × (1 − p/100). Here a decrease has 0 < p < 100, so something positive remains.
When the values being compared are themselves percentages, their numerical difference is measured in percentage points. Their relative percentage change still uses the original percentage as the denominator. Percentage points and relative percentage change answer different questions; neither label can replace the other.
Worked example 1
A ₹1,600 chair increases in price by 12%. Find the new price.
The increase is 1600 × 12/100 = ₹192. Add it to the original: 1600 + 192 = ₹1792. Equivalently, 1600 × 1.12 = ₹1792. The multiplier includes both the original price and its increase.
Worked example 2
A price falls from ₹2,250 to ₹1,980. Find the percentage decrease.
The reduction is 2250 − 1980 = ₹270. Relative to the original, (270/2250) × 100% = 12%. Checking, 2250 × 0.88 = 1980. Using the final price as denominator would not measure the original percentage decrease.
Worked example 3
A course completion rate rises from 40% to 52%. Describe the change in both ways.
The difference is 52 − 40 = 12 percentage points. The relative increase is (12/40) × 100% = 30%. Thus the rate rose by 12 percentage points, or by 30% of its original value, not by the same numerical percentage in both descriptions.
Common traps
Use the original base consistently. Do not report only the amount added when asked for the final amount. Reserve “percentage points” for differences between percentages, not ordinary differences in money or volume.
Practice questions
- A ₹2,400 fee increases by 15%. Find the new fee.
- A tank contains 16 L of water. Remove 6.25% of this water. Find the remaining volume.
- A price increases from ₹960 to ₹1,104. Find the percentage increase.
- A rate falls from 75% to 60%. Find the decrease in percentage points and the relative percentage decrease.
Worked answers
- The increase is 2400 × 0.15 = ₹360. Adding it gives 2400 + 360 = ₹2760, the new fee.
- Since 6.25% = 1/16, remove 16 × 1/16 = 1 L. The remaining volume is 16 − 1 = 15 L.
- The increase is 1104 − 960 = ₹144. Divide by the original price: (144/960) × 100% = 15%.
- The rate falls by 75 − 60 = 15 percentage points. Relative to its starting value, the decrease is (15/75) × 100% = 20%.