3. Percentage and successive change
Free study material · concepts, shortcuts & solved questions
Percentage means “per hundred.” If a quantity changes by a% and then b%, net percentage change = a+b+ab/100, taking a decrease as negative. A percentage of a base and a percentage-point change are different: a rate moving from 20% to 25% rises by 5 percentage points but by 25% relative to its old rate.
Method before formula Use a base of 100 when no amount is given. For reverse percentage, divide by the multiplier: after a 20% increase, original = final/1.20. This denominator is a common SSC trap. |
Formula and decision table
Situation | Multiplier |
Increase p% | 1+p/100 |
Decrease p% | 1−p/100 |
Successive +20%, −20% | 1.2×0.8=0.96, net 4% decrease |
Worked understanding
A reliable solution has five visible moves: identify the data, choose the base or unit, write the rule, substitute carefully, and check the size of the answer. The examples in this chapter are deliberately small so that the method remains visible.
Calculation discipline Before pressing ahead, state the denominator or unit in words. For example: profit on CP, discount on MP, average over number of items, speed in metres per second, and probability over the fixed sample space. |
Solved examples from this chapter
Question focus | Correct move | Answer |
A value rises 20% and falls 20%. Net change is: | The multiplier is 1.2×0.8=0.96. | C. 4% decrease |
After a 25% increase a value is 500. Original value: | 500/1.25=400. | B. 400 |
From 40% to 50%, the percentage-point increase is: | 50−40=10 percentage points. | A. 10 |
What an examiner is testing
The options around Percentage and successive change usually represent a wrong base, a missed conversion, a sign error or a shortcut used outside its condition. Say the base and unit before calculating, estimate the result, and use substitution or a reverse operation as the final check.
Step-by-step answer construction
Example 1: A value rises 20% and falls 20%. Net change is: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is 4% decrease, because The multiplier is 1.2×0.8=0.96.
Example 2: After a 25% increase a value is 500. Original value: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is 400, because 500/1.25=400.
Example 3: From 40% to 50%, the percentage-point increase is: First identify the requested quantity and its base or unit. Apply the chapter rule, keep the operation visible, estimate the expected range, and compare the result with the options. The correct answer is 10, because 50−40=10 percentage points.
Chapter practice
1. A value rises 20% and falls 20%. Net change is:
(A) 0% (B) 2% decrease (C) 4% decrease (D) 4% increase
Answer: C. 4% decrease | Explanation: The multiplier is 1.2×0.8=0.96.
2. After a 25% increase a value is 500. Original value:
(A) 375 (B) 400 (C) 425 (D) 625
Answer: B. 400 | Explanation: 500/1.25=400.
3. From 40% to 50%, the percentage-point increase is:
(A) 10 (B) 20 (C) 25 (D) 90
Answer: A. 10 | Explanation: 50−40=10 percentage points.
SSC CGL speed and trap clinic
For Percentage and successive change, speed comes after classification. Before calculating, say aloud what the number means, what the denominator is, and what unit the answer must carry. Then use the nearest-option check to catch a sign, base or conversion error.
Checkpoint | What to verify | Typical SSC mistake |
Base | Which quantity is the base in Percentage and successive change? | Using selling price instead of cost price, or part instead of total |
Unit | Are time, distance, area and rate in compatible units? | Mixing hours with minutes or km/h with m/s |
Direction | Should the answer increase, decrease or stay bounded? | Accepting an impossible negative length or probability above 1 |
Estimate | What range should the answer lie in before exact work? | Trusting a long calculation that is far from the options |
Reverse check | Can the answer be substituted back into the condition? | Stopping at an algebraic value without verification |
Mini decision drill
1. Write the first operation you would perform in a Percentage and successive change question and why.
2. State the most dangerous denominator or unit in this chapter.
3. Give one condition under which a shortcut would be invalid.
4. Create a small numerical example and verify it by a second method.
Revision evidence Do not tick this chapter because you recognised the formula. Tick it only after you solve one direct question, one altered-condition question and one mixed-paper question correctly. |