Mathematics: Speed Through Formula Recall
What to master
Number system (divisibility rules, HCF/LCM, remainders), percentages, ratio and proportion, averages, profit and loss, simple and compound interest, time–speed–distance, time and work, mensuration of 2D and 3D figures, elementary algebra, and height-and-distance trigonometry. Army questions favour direct application of a formula, so marks come from instant recall rather than long derivation.
Traps that cost marks
- Percentages: always fix the base. A 25% rise followed by a 20% fall does not bring you back to the original value.
- Successive discounts of a% and b% are not (a+b)%. The single equivalent is a + b − ab/100.
- Average speed over equal distances uses the harmonic mean 2xy/(x+y), not (x+y)/2.
- Time and work: convert days into work-per-day units (A does 1/12 per day) before adding rates.
- Mensuration: convert units before multiplying, and remember 1 litre = 1000 cm³.
Worked example
A shopkeeper marks an article 40% above cost and allows 25% discount. Find profit percent. Let cost = 100. Marked price = 140. Selling price = 140 × 0.75 = 105. Profit = 5 on 100, so 5%.
Rule of thumb: when a problem is stated only in percentages, take the starting quantity as 100 and convert every step into rupees or units. This single habit removes most careless errors in arithmetic sections.