Study Guide · Chapter 31
9. Common Mistakes Aspirants Make
Free study material · concepts, shortcuts & solved questions
Select any text to highlight or save it
- Confusing direct and inverse proportion. Many students apply “more men, more days” (direct) instead of the correct inverse relationship “more men, fewer days.” Rule of thumb: if increasing one quantity naturally causes the other to decrease (like men vs. days, or speed vs. time), it is inverse proportion — use product = constant, not ratio = constant.
- Forgetting to convert units before forming a ratio. Comparing 2 hours to 50 minutes directly as 2:50 without converting hours to minutes (120:50) is a very common slip.
- Not reducing the ratio to lowest terms, leaving an answer like 12:18 instead of 2:3 — this can make an MCQ option look “wrong” even when the calculation is correct.
- Errors while converting two separate ratios into one continued ratio — students often forget to make the common term equal (via LCM) before merging a:b and b:c into a:b:c, leading to an incorrect combined ratio.
- Applying simple partnership rules (investment ratio only) to compound partnership problems where investment durations differ — profit must be divided by (Investment × Time), not investment alone.
- Sign errors in componendo-dividendo, especially forgetting that (a−b) can be negative depending on which is larger — always double check by substituting back numbers.
- Forgetting to reduce the compound ratio at the end after multiplying several ratios together — a compound ratio like 8 : 15 : 20 might still share a common factor that needs to be cancelled before it is presented as the “final” answer.
- Treating “x% more than” and “x% of” as the same thing when converting percentage statements to ratios — “A is 20% more than B” gives A:B = 120:100, not 20:100.
- Assuming mean proportional is the arithmetic average (a+c)/2 instead of the geometric mean √(ac). These give very different values and this mix-up is extremely common.
- Losing track of which term is “third proportional to a, b” vs “third proportional to b, a” — order matters: third proportional to a and b uses formula b²/a, not a²/b.
- In age problems, adding/subtracting the same number of years to only one age instead of both — the “x years ago/hence” condition must be applied identically to every person’s age in the ratio.
- Rounding off ratio values mid-calculation (e.g., rounding a fraction to two decimal places) before comparing ratios — this can flip the comparison result; always use cross-multiplication for exact comparison instead.
- Mishandling the “value of one part” when the total is not evenly divisible by the sum of ratio terms — instead of leaving an untidy fraction, aspirants sometimes round the “1 part” value early, which then compounds into a larger error across all shares. Keep 1 part as an exact fraction until the final step, or verify that the total given in the question is indeed divisible by the sum of the ratio terms.
- Ignoring the direction of a difference in “A gets more than B by ₹X” type questions. The difference must be taken as (larger ratio term − smaller ratio term) × (value of one part) = X; reversing which term is larger changes the sign and gives an impossible (negative) total.
Page 1 of 1