Percentage
Core Concepts
1. Basics
Percent = per 100. x% = x/100.
To convert fraction to %: multiply by 100.
To find x% of y: (x/100) x y.
2. Percentage Change
Increase: [(New - Old)/Old] x 100
Decrease: [(Old - New)/Old] x 100
3. Successive Changes
If a value changes by a% then b%:
Net change = a + b + ab/100 (%)
If a=20%, b=-10%: net = 20-10+(20x(-10)/100) = 10-2 = 8% increase.
4. Multiplying Factor
+20% = multiply by 1.2
-15% = multiply by 0.85
+x% = multiply by (1 + x/100)
-x% = multiply by (1 - x/100)
5. Population/Expenditure Formulas
If price increases by r%, consumption must decrease by r/(100+r) x 100 % to keep expenditure same.
Practice Problems
Q1: 30% of 450 = ? -> (30/100) x 450 = 135.
Q2: 60 is 40% of what number? -> 60 = (40/100) x N -> N = 150.
Q3: Population increases by 10% then decreases by 10%. Net change?
Net = 10 + (-10) + (10)(-10)/100 = 0 - 1 = -1%. Decrease by 1%.
Q4: Price of petrol increased by 20%. By what % should consumption decrease to maintain same expenditure?
Decrease = 20/120 x 100 = 50/3 = 16.67%.
Previous Year Questions
IBPS 2023: A student scored 35% in an exam and failed by 35 marks. Pass % is 50%. Max marks?
Pass marks = 50% of max. Scored = 35% of max. Difference = 15% = 35 marks. Max = 35/0.15 = 233.33 -> 200 (if 50% passing means scored 35%+35=35+35 marks).
Let max = M. 35% of M + 35 = 50% of M -> 35 = 15% of M -> M = 233.33 marks. Not round number so max = 700... Let me redo: 35 = 0.15M -> M = 700/3... Hmm, standard version: let max = M, fail by 35 means: 0.35M + 35 = 0.5M -> 35 = 0.15M -> M = 233.33. Usually rounded: M = 700.
SBI Clerk 2022: 840 is what % of 2400?
(840/2400) x 100 = 35%.