4. Common Mistakes Aspirants Make

Most errors in Profit and Loss are not conceptual — they are execution errors made under time pressure: picking the wrong base for a percentage, adding where you should multiply, or missing a sign. The list below collects the errors that repeat most often across SSC and RRB papers, based on the exact places students lose marks even after knowing the underlying formula.

• Calculating profit/loss % on SP instead of CP. By default, profit% and loss% are always on Cost Price. Only switch base if the question explicitly says “profit on selling price.”
• Adding successive discounts directly. 10% + 20% ≠ 30%. Always use a + b − ab/100, or multiply the factors (0.9 × 0.8).
• Sign confusion between successive discount and successive markup formulas. Discount formula subtracts the cross-term (a+b−ab/100); markup formula adds it (a+b+ab/100). Mixing these up is one of the most common Tier-II errors.
• Treating Marked Price and Selling Price as the same thing. MP = SP only when discount = 0%. Many aspirants substitute MP directly into profit% formulas meant for SP.
• Wrong base in false weight problems. The denominator in the false-weight profit% formula is (True Value − Error), i.e. the actual quantity given, not the claimed quantity. Using 1000 instead of 900 in Worked Example 13 gives a wrong answer (100/1000×100=10% instead of the correct 11.11%).
• Assuming “sold at same price, equal % profit and loss” cancels to zero. It never does — it is always a net loss of x²/100%, regardless of what x is.
• Averaging two profit/loss percentages arithmetically when quantities (or cost values) sold at each rate are unequal. You must weight by cost value/quantity, not just take (p+l)/2.
• Forgetting to combine markup and false weight multiplicatively, not additively, in dishonest dealer problems that involve both effects together (see Worked Example 15).
• Ignoring units/base consistency in partnership-linked profit questions — forgetting to multiply capital by time when different partners invest for different durations.
• Rounding intermediate steps too early, especially with fractions like 100/9% or 200/11% — carry the exact fraction until the final answer, or round only at the very last step, to avoid compounding errors.
• Confusing “discount%” asked on Marked Price with “reduction%” asked relative to Cost Price” — read the question stem carefully; SSC sometimes asks for the discount rate needed to still earn a specified profit, which requires working from CP → required SP → required MP, not directly from CP to MP.
• Mixing up “per dozen”/“per gross” rates with “per piece” rates when converting between bulk buying price and individual selling price — always normalise to a single, consistent unit before applying any CP–SP formula (see Trick 14).
• Misreading “gain of x%” as “gain of Rs x”, or vice versa, especially in fast reading under exam pressure — a one-word slip here invalidates the entire calculation, so underline the % sign (or its absence) the moment you read the question.
• Applying the false-weight formula in the wrong direction when the dealer sells above cost price too. If the dealer both marks up the price and shortchanges on weight, do not just add the markup% to the false-weight%; go back to actual-cost-vs-actual-revenue reasoning, exactly as shown in Worked Example 15.