Numerical Ability: Arithmetic Shortcuts and Accuracy
Syllabus weight
Numerical Ability in HSSC CET stays at matriculation level: percentage, ratio and proportion, average, profit and loss, simple and compound interest, time and work, speed and distance, mixtures, and areas and volumes. Data interpretation appears as tables or bar charts.
Fast rules
- Percentage change: an increase and decrease of the same x% gives a net decrease of x²/100 %. A 20% rise then a 20% fall gives a 4% net fall.
- Profit and loss: take cost price as 100. Selling price = CP × (100 + profit%)/100.
- Successive discounts: a% and b% give a single discount of a + b − ab/100.
- Time and work: convert days into units per day. If A does 1/12 and B does 1/18 per day, together they do 5/36, so the work takes 36/5 = 7.2 days.
- Speed: 1 km/h = 5/18 m/s; 1 m/s = 18/5 km/h.
- Average: total = average × count; adding a value equal to the average leaves the average unchanged.
Worked example
A shopkeeper marks an article 40% above cost and gives a 25% discount. Find the profit percentage. Let CP = 100. Marked price = 140. Selling price = 140 × 0.75 = 105. Profit = 5%. The tempting wrong answer is 15% (40 − 25), which ignores that the discount applies to the marked price, not the cost price.
Traps
- Applying the discount to CP instead of MP.
- Using the simple interest formula for compound interest over more than one year.
- Mixing the speed of a boat in still water with the speed of the stream.
- Using diameter in place of radius in mensuration; check units before computing.