SSC CPO Quantitative Aptitude: Percentage Bases and Successive Changes
Learn to track percentage bases, reverse changes and profit or discount calculations with worked examples and a practical error review routine.
Percentages look simple until the reference value shifts. A 20% rise followed by a 20% fall does not restore the starting value; a discount and a profit can each use a different base. The reliable habit is to identify what each percentage is “of” before calculating.
The Staff Selection Commission's Sub-Inspector examination notice includes quantitative aptitude topics such as percentages, ratio and proportion, profit and loss, and discount. Use the official SSC website and SSC CPO notice for exam context. The linked notice is a historical reference, not a claim about current dates, marking or vacancies. Check the applicable notice for your examination.
The base is the key
A percentage change is calculated against the value immediately before that change:
Change amount = percentage rate as a fraction × current base.
For successive changes, use a multiplier each time. An increase of r% means multiplying by 1 + r/100; a decrease means multiplying by 1 − r/100. The second change applies to the updated value, not automatically to the original.
For an increase of a% followed by a decrease of b%, the overall multiplier is (1 + a/100) × (1 − b/100). Adding or subtracting the rates treats them as if they shared one base. That shortcut generally fails.
Three original worked examples
These are hypothetical practice questions, not extracted SSC past-paper questions. The prices and allowance illustrate the arithmetic only.
1. Successive increase and decrease
An allowance of ₹8,000 rises by 15%, then falls by 10%. What is the final allowance and the net percentage change?
- After the increase: ₹8,000 × 1.15 = ₹9,200.
- After the decrease: ₹9,200 × 0.90 = ₹8,280.
- Net increase: ₹8,280 − ₹8,000 = ₹280.
- Net percentage change: 280 ÷ 8,000 × 100 = 3.5% increase.
The tempting shortcut “15% − 10% = 5% increase” fails because the decrease is taken from ₹9,200, not ₹8,000. As an independent check, multiply 1.15 × 0.90 = 1.035. That final multiplier confirms a 3.5% increase.
2. Reverse percentage
After a 20% reduction, a jacket costs ₹1,440. Find its original price.
The reduced price is 80% of the original. Let the original be P:
0.80 × P = ₹1,440, so P = ₹1,440 ÷ 0.80 = ₹1,800.
Check forward: 20% of ₹1,800 is ₹360, and ₹1,800 − ₹360 = ₹1,440. Adding 20% of ₹1,440 gives ₹1,728, which is incorrect because it uses the reduced price as the percentage base.
The distinction also explains why recovery percentages differ: returning from ₹1,440 to ₹1,800 requires a rise of ₹360 on a ₹1,440 base, or 25%, not 20%.
3. Discount and profit use different bases
A shopkeeper buys a bag for ₹1,000, marks it 25% above cost, then gives a 10% discount on the marked price. Find selling price and profit percentage.
- Marked price: ₹1,000 × 1.25 = ₹1,250.
- Discount: 10% of ₹1,250 = ₹125.
- Selling price: ₹1,250 − ₹125 = ₹1,125.
- Profit: ₹1,125 − ₹1,000 = ₹125.
- Profit percentage: 125 ÷ 1,000 × 100 = 12.5%.
The discount uses marked price; the profit percentage uses cost price. Calculating the discount as 10% of cost would incorrectly give a selling price of ₹1,150. Calculating profit percentage on selling price would answer a different measure from the conventional profit-on-cost question.
Diagnose the error before repeating the question
Label each mistake as wrong base, wrong multiplier, reversed operation, or arithmetic slip. A wrong-base error needs a different correction from a multiplication error. Write “10% of marked price” beside the rate, rather than recording only “10%.”
Estimate the direction first. A discounted price must be below marked price; reversing a reduction should produce a larger original; equal positive and negative percentage changes should leave the original lower. These checks do not replace calculation, but they catch contradictions.
Create a compact review table: starting quantity, percentage base, operation, final quantity and verification. For reverse questions, verify by applying the change forward. For successive questions, compare the final amount with the original rather than the intermediate amount.
Build a flexible practice routine
In a short session, review one rule and solve a few untimed examples. In a longer session, mix successive changes, reverse percentages and discount-profit problems so the question wording—not the order in your worksheet—determines the method.
Redo missed questions without looking at solutions. Then change one number or reverse the question to test whether you learned the relationship. Track repeated base errors alongside accuracy; a correct guess is not evidence that the reasoning is secure.
Use our SSC CGL mock-test error-analysis guide for a broader review method, and browse Scholareum exam resources and test series for relevant practice. Confirm the selected series matches your exam and topic requirements.
Frequently asked questions
Why do equal percentage increases and decreases not cancel?
They act on different values. A 20% increase followed by a 20% decrease gives 1.20 × 0.80 = 0.96, leaving the starting amount 4% lower.
How do I reverse a percentage decrease?
Divide the final value by the remaining fraction. After a 20% decrease, divide by 0.80 rather than multiplying the final amount by 1.20.
What base should I use for profit percentage?
Use cost price: profit ÷ cost price × 100. A discount uses marked price when the question explicitly describes a discount on that marked price.
Official references
Visit the SSC website for current official notices. The 2025 Sub-Inspector notice is cited for syllabus context only. All worked examples above are original practice material.