Theory & Concepts
SSC CGL Successive Percentage Change Questions & Tricks
Prepare Successive Percentage Change for SSC CGL with formulas, short tricks, solved examples, practice questions, PYQs, and free PDF notes for faster exam preparation.
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Practice Notes
20 min readDifficulty: Intermediate
Successive percentage change is the engine behind Compound Interest, Population Growth, and Depreciation. Mastering this tool allows you to bypass multi-step calculations with a single formula.
Whether it's a 2D area change or a 3D volume shift, the ratio-based "AB Formula" provides the fastest route to the final answer in Ssc cgl Tier-1 and Tier-2 exams.
Learning path
- The master AB formula
- 3D Volume (iterative) logic
- Equivalent discount shortcut
- 10 standard solved problems
- Fractional percentage ratio method
1. The AB Formula (2-Step Change)
If a quantity changes by and then by , the net percentage change is:
Important Rule:
- Use positive (+) value for increase/profit.
- Use negative (-) value for decrease/discount.
2. The 3D iterative logic (Volume)
For 3rd degree shifts (like volume of a sphere or cylinder), apply the formula twice:
Step 1: Apply formula to first two changes to get .
Step 2: Apply formula between and the third change.
Example: 10% increase in sphere radius. Step 1: 10 + 10 + 1 = 21%. Step 2: 21 + 10 + 2.1 = 33.1%.
3. 10 Solved examples
Question 01Standard pattern
Salary of a person was increased by 20% and then decreased by 20%. Find his net salary change.
4% decrease
4% increase
No change
1% decrease
Correct answer: a) 4% decrease
Solution
Here \( a = 20 \) and \( b = -20 \).
Net change = \( 20 - 20 + \frac{20 \times (-20)}{100} \).
Calculation: \( 0 - 4 = -4\% \).
Result = \( 4\% \text{ decrease} \).
Question 02Standard pattern
What is a single discount equivalent to two successive discounts of 20% and 10%?
28%
30%
25%
26%
Correct answer: a) 28%
Solution
For discount, use negative values: \( a = -20, b = -10 \).
Calculation: \( -20 - 10 + \frac{(-20) \times (-10)}{100} \).
Result: \( -30 + 2 = -28\% \).
Question 03Standard pattern
The length and breadth of a rectangle are increased by 20% and 30% respectively. Find percentage increase in area.
56%
50%
60%
44%
Correct answer: a) 56%
Solution
Calculation: \( 20 + 30 + (20 \times 30)/100 = 50 + 6 = 56\% \).
Question 04Standard pattern
The radius of a sphere is increased by 10%. What is the percentage increase in its volume?
33.1%
21%
30%
31%
Correct answer: a) 33.1%
Solution
Volume depends on \( r^3 \). We need three iterations of 10%.
Step 1 (Area): \( 10 + 10 + 1 = 21\% \).
Step 2 (Volume): \( 21 + 10 + (21 \times 10)/100 = 33.1\% \).
Question 05Standard pattern
The price of sugar is increased by 32%. A family reduces consumption so that expenditure increases by only 10%. If current consumption is 30 kg, find original consumption.
36 kg
35 kg
40 kg
32 kg
Correct answer: a) 36 kg
Solution
Formula: \( \frac{C_1}{C_2} = \frac{100 + E%}{100 + P%} \)? No, Ratio Method is better.
Price Ratio: \( 100 : 132 \). Exp Ratio: \( 100 : 110 \).
Cons Ratio = \( Exp / Price = 110 / 132 = 5/6 \).
Current (5 units) = 30 kg. 1 unit = 6 kg.
Original (6 units) = \( 6 \times 6 = 36 \text{ kg} \).
Question 06Standard pattern
Length of a rectangle increases by 10% and area increases by 21%. Find change in breadth.
10% increase
11% increase
5% increase
12% increase
Correct answer: a) 10% increase
Solution
Eq: \( 10 + x + 10x/100 = 21 \).
\( 1.1x = 11 \implies x = 10 \).
Question 07Standard pattern
Side of a cube is increased by 50%. Find percentage increase in volume.
237.5%
125%
150%
225%
Correct answer: a) 237.5%
Solution
Apply 50% three times.
Step 1: \( 50 + 50 + 25 = 125\% \).
Step 2: \( 125 + 50 + (125 \times 50)/100 = 175 + 62.5 = 237.5\% \).
Question 08Standard pattern
Radius of cone increased by 10% and height decreased by 20%. Net change in volume?
3.2% decrease
3.2% increase
5% decrease
No change
Correct answer: a) 3.2% decrease
Solution
\( r^2 \) change = 21% increase.
Volume with h: \( 21 - 20 - (21 \times 20)/100 = 1 - 4.2 = -3.2\% \).
Question 09Standard pattern
Equivalent single increase for successive increases of 20% and 25%.
50%
45%
60%
44%
Correct answer: a) 50%
Solution
Calculation: \( 20 + 25 + (20 \times 25)/100 = 45 + 5 = 50\% \).
Question 010Standard pattern
Population of a town is 10,000. It increases by 10% first yr and decreases by 10% second yr. Net population?
9,900
10,000
9,800
11,000
Correct answer: a) 9,900
Solution
Net change = 1% decrease.
Calculation: \( 0.99 \times 10000 = 9900 \).
4. Strategy errors to avoid
Error 01Addition trap: Adding 20% and 30% to get 50% instead of using the successive formula.
Error 02Negative oversight: Forgetting to put a minus (-) sign for discounts or decreases in the AB formula.
Error 03Volume neglect: Only calculating the area increase (r^2) when the question asks for volume increase (r^3).
Error 04Fractional delay: Using the AB formula for complex fractions like 16.66% instead of the Ratio Method.
