3. Shortcuts and Speed Tricks

Trick 1 — Assume CP = 100. Whenever actual rupee values are not given (only percentages/ratios), let CP = 100. All subsequent numbers become simple percentages, eliminating fraction arithmetic. Example: “An article is sold at 20% profit; if it had been bought at 10% less and sold for Rs 5 less, profit would have been 30%.” Let CP=100 → SP=120. New CP=90, new SP=115, new profit=25/90×100≈27.7%… (illustrative use only — always assume CP=100 first before introducing other unknowns).

Trick 2 — Multiplying Factor for CP↦︎SP. Don’t write “Profit% = (SP−CP)/CP × 100” every time. Instead directly use SP = CP × (100+p)/100 or CP = SP × 100/(100+p). This single-line jump saves 15–20 seconds per question.

Trick 3 — Successive Discount Formula. For two discounts a% and b%: Effective% = a + b − ab/100. Never add discounts directly — a 20% + 10% discount is 28%, not 30%. This is one of the most heavily tested traps.

Trick 4 — Successive Markup Uses the Same Formula. If price is increased by a% and then again by b%, the net increase is also a + b + ab/100 (note the plus sign for two successive increases, since both factors are >1). E.g., two successive 10% hikes give net = 10+10+1 = 21% increase, not 20%.

Trick 5 — Markup Then Equal Discount Always Gives Net Loss. If CP is marked up by r% and then discounted by the same r%, SP = CP(1+r/100)(1−r/100) = CP(1 − r²/10000). Net result is always a loss of r²/100 % — never break-even. E.g., mark up 20%, discount 20% → net loss = 400/100 = 4%.

Trick 6 — CP:SP Ratio Gives Profit% Directly. If CP : SP = a : b, then Profit% = [(b−a)/a] × 100 (or Loss% = [(a−b)/a] × 100 if a > b). No need to assume actual values. Example: CP:SP = 4:5 ⇒ Profit% = (1/4)×100 = 25%.

Trick 7 — False Weight Quick Formula. If a dealer uses w grams instead of 1000 g while selling at cost price: Profit% = [(1000−w)/w] × 100. Memorise this single line — false weight questions become 10-second solves. Example: w = 800 g → Profit% = 200/800 × 100 = 25%.

Trick 8 — Same SP, Equal % Profit/Loss ⇒ Always Net Loss = (x/10)². Whenever you spot “sold at the same price, gain x% on one, lose x% on the other,” instantly write Loss% = x²/100 without computing individual CPs. Example: x = 25 ⇒ Loss% = 625/100 = 6.25%.

Trick 9 — Effect of a Change in SP on Profit%. If increasing SP by Rs ‘a’ changes profit from p₁% to p₂% (on the same CP), then: > CP = a × 100/(p₂ − p₁) Example: Selling for Rs 60 more increases profit from 20% to 35%. CP = 60×100/15 = Rs 400. Why it works: SP₂ − SP₁ = CP×(1+p₂/100) − CP×(1+p₁/100) = CP×(p₂−p₁)/100. Rearranging directly gives CP = (SP₂−SP₁)×100/(p₂−p₁), which is the formula above with a = SP₂−SP₁. Recognising this pattern instantly (rather than setting up “let CP = x” and solving a linear equation from scratch) is what separates a 10-second solve from a 60-second one on this exact question type.

Trick 10 — Fraction Trick for “Sold at 2/3 of MP” type questions. Convert the fraction directly to a percentage of MP rather than introducing a separate discount variable — e.g., “sold at 3/4 of MP” simply means SP = 0.75 × MP, so treat 0.75 as your discount multiplying factor straightaway (this is what Worked Example 21 used).

Trick 11 — When Profit% Equals Discount% (special coincidence check). If a problem states markup% = m and discount% = d turn out to be numerically equal to the resulting profit%, verify quickly using SP=CP(1+m/100)(1−d/100) rather than assuming any shortcut relationship — there is no general shortcut here; this is a reminder trick to avoid a false pattern-matching trap.

Trick 12 — Weighted Average for Mixed Profit/Loss Lots. When part of a lot is sold at profit p% and the rest at loss l% in the ratio of quantities m:n (assuming same per-unit CP), the overall % change is the CP-weighted average: > Overall% = (m×p − n×l)/(m+n) [positive = net profit, negative = net loss] Example: 60kg at +20%, 40kg at −10%, ratio 60:40 = 3:2. Overall% = (3×20 − 2×10)/5 = (60−20)/5 = 8% profit (matches Worked Example 18). This is simply Trick 1 (CP=100) applied twice and combined — derive it yourself once so you trust it, then use it directly in the exam without re-deriving each time.

Trick 13 — Backsolving from Options (option-elimination). SSC and RRB papers are MCQ-based, so whenever a question asks you to find CP, MP, or a weight/quantity, and the algebra looks like it will take more than two steps, plug the given options back into the question statement instead of solving forward. This is especially fast for “find CP such that…” questions like Worked Examples B9 and B13 — substituting an option often confirms the answer in fewer keystrokes than isolating the variable algebraically.

Trick 14 — Unitary Method for “Rate per Dozen/Rate per Unit” Questions. When a question gives cost “per dozen” or “per gross” but asks about profit on individual pieces (or vice versa), immediately convert everything to a per-unit basis before applying any profit/loss formula. Mixing “per dozen” and “per piece” figures in the same equation is a common source of factor-of-12 errors — always normalise units first, exactly as you would in a Time & Work or Ratio problem.