Percentage and Fraction Tricks

Percentage Tricks

Basic Conversion:
- To convert a percentage to a fraction: Divide by 100.
- Example: 25% = 25/100 = 1/4.
Finding Percentages:
- To find X% of a number: Multiply the number by X and divide by 100.
- Example: 30% of 200 = (30/100) × 200 = 60.
Percentage Increase/Decrease:
- Increase = Original × (1 + Percentage/100).
- Decrease = Original × (1 - Percentage/100).
Quick Approximation:
- 10% of any number is easy: Just move the decimal one place left.
- For 5%, halve the 10% value.

Fraction Shortcuts

Common Fractions:
- 1/2 = 0.5, 1/3 ≈ 0.33, 1/4 = 0.25, 1/5 = 0.2.
Addition/Subtraction of Fractions:
- Find a common denominator.
- Example: 1/3 + 1/4 = (4 + 3)/12 = 7/12.
Multiplication of Fractions:
- Multiply numerators and denominators directly.
- Example: (2/3) × (3/4) = 6/12 = 1/2.
Division of Fractions:
- Multiply by the reciprocal: (a/b) ÷ (c/d) = (a/b) × (d/c).

Time And Work Methods

Work Formula:
- Work = Time × Rate.
Joint Work:
- If A can complete work in A days and B in B days, they can together finish it in:
- Time = (A × B) / (A + B).
Effort Calculation:
- Man-hours = Total Work needed.
- Example: 10 workers can finish a job in 5 days; total man-hours = 10×5 = 50.
Fraction of Work Done:
- If A does 1/5 of a job in 1 day and B does 1/10, their combined effort in a day = 1/5 + 1/10 = 3/10.

Average Calculations

Average Formula:
- Average = (Sum of observations) / (Number of observations).
Finding Average Quickly:
- If data points increase or decrease by a constant factor, adjust the average accordingly.
Average of Consecutive Numbers:
- Average of n consecutive numbers is the middle value.
Weighted Average:
- Weighted Average = (Sum of weighted values) / (Total weights).
- Example: If scores are 50 (weight 2) and 100 (weight 3), weighted average = (50×2 + 100×3) / (2+3) = 80.

Ratio And Proportion Techniques

Ratios:
- A ratio compares two quantities (a:b).
- Simplification: Divide both quantities by their GCD.
Proportions:
- Proportion states that two ratios are equal (a/b = c/d).
- Cross Multiplication: a × d = b × c.
Solving Problems with Ratios:
- If a:b = c:d, then a×d = b×c.
- Use the concept to find missing values.
Combining Ratios:
- If two ratios are A:B and B:C, the combined ratio A:B:C is derived by making sure the middle term is the same.

These shortcuts and tricks can aid in solving quantitative problems quickly during the IBPS examination. Practice regularly to enhance speed and accuracy.

Percentage Tricks

Converting a percentage to a fraction: divide the percentage by 100. For example, 25% = 25/100 = 1/4.
Finding a percentage of a number: multiply the number by the percentage and divide by 100. For example, 30% of 200 = (30/100) × 200 = 60.
Percentage increase = original amount × (1 + percentage/100)
Percentage decrease = original amount × (1 - percentage/100)
10% of any number is found by moving the decimal one place to the left.
5% is half the value of 10%.

Fraction Shortcuts

Common fractions 1/2 = 0.5, 1/3 ≈ 0.33, 1/4 = 0.25, 1/5 = 0.2
To add or subtract fractions find a common denominator
To multiply fractions multiply numerators and denominators
To divide fractions multiply by the reciprocal: (a/b) ÷ (c/d) = (a/b) × (d/c)

Time And Work Methods

Work = Time × Rate
If A can complete a task in A days and B in B days, they can complete it together in: Time = (A × B) / (A + B)
Man-hours = Total Work Needed. For example: 10 workers complete a job in 5 days; total man-hours = 10×5 = 50
If A does 1/5 of a job in 1 day and B does 1/10 in a day, their combined effort is: 1/5 + 1/10 = 3/10

Average Calculations

Average = (Sum of observations) / (Number of observations)
If data points increase or decrease by a constant factor, adjust the average accordingly
The average of n consecutive numbers is the middle value
Weighted Average = (Sum of weighted values) / (Total weights). For example, if scores are 50 (weight 2) and 100 (weight 3), the weighted average = (50×2 + 100×3) / (2+3) = 80.

Ratio And Proportion Techniques

A ratio compares two quantities (a:b).
Simplify a ratio by dividing both quantities by their Greatest Common Divisor (GCD)
A proportion states that two ratios are equal (a/b = c/d)
Cross Multiplication: a × d = b × c
If a:b = c:d, then a×d = b×c. Use this concept to find missing values in problems.
If ratios are A:B and B:C, the combined ratio is A:B:C. Find the combined ratio by ensuring the middle term is the same in both ratios.