Questions
4–6 questions in major competitive exams
Difficulty
Medium
Importance
High yield for SSC and banking clerical cadres
Overview
Arithmetic Word Problems form the backbone of quantitative aptitude for Indian government exams, bridging the gap between basic calculation and logical reasoning. Mastering these allows candidates to translate real-world scenarios into mathematical expressions quickly, which is essential for scoring in the strict time constraints of exams like SSC CGL and IBPS.
Percentages and Profit & Loss
These topics revolve around base values and percentage changes. For exam success, move away from long-form algebraic equations and focus on fraction-to-percentage conversions to accelerate calculations.
- Fraction to percentage conversion table (1/2 to 1/20)
- Successive percentage change formula: (a+b + ab/100) percent
- Profit percent = (Gain/Cost Price) * 100
- Marked Price - Discount = Selling Price
- Effect of successive discounts on net price
Time, Speed, and Distance
This subtopic tests your ability to handle relative speed and unit conversions. It is critical to convert all units into m/s or km/hr consistently before performing arithmetic operations.
- Distance = Speed * Time
- Average Speed = (2 * S1 * S2) / (S1 + S2) for equal distances
- Relative Speed: S1+S2 (opposite), |S1-S2| (same direction)
- Convert km/hr to m/s by multiplying by 5/18
- Trains passing objects: length of train + length of platform
Time and Work
Efficiency-based problems require you to treat total work as a constant or the Least Common Multiple (LCM) of the given times. This method drastically reduces the complexity of variable-heavy equations.
- Total Work = Efficiency * Time
- Individual efficiency = Total Work / Time taken
- If A takes x days and B takes y days, A+B finish in (xy)/(x+y) days
- M1D1H1 / W1 = M2D2H2 / W2 (Chain Rule)
- Work done by women/men/children based on ratios
Ratio, Proportion, and Ages
Ages and ratios are solved most effectively using multiplier variables. Always check if the ratio provided is for the present, past, or future to avoid phase-based calculation errors.
- Cross-multiplication method for age ratio problems
- Mean proportional of a and b is square root of (ab)
- Componendo and Dividendo rule
- Maintaining age gap consistency (age difference remains constant)
- Direct and Inverse variation relationships
Formula Sheet
Distance = Speed * Time
Total Work = Efficiency * Time
Successive Change = x + y + xy/100
Average Speed = Total Distance / Total Time
Profit = Selling Price - Cost Price
Exam Tip
Instead of solving for 'x', use the ratio-multiplier method or the LCM method to bypass heavy arithmetic and save at least 30 seconds per question.
Common Mistakes
- Failing to convert units (e.g., mixing km/hr with seconds) leading to incorrect distance values.
- Applying simple interest logic to compound interest problems or vice-versa.
- Misinterpreting 'more than' or 'less than' phrasing in ratio and percentage questions.
More Revision Notes
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