BCS Written Math & Mental Ability common mistakes
BCS Written Math & Mental Ability · Understand the traps and how to avoid them.
When finding the LCM of fractions, the candidate computes LCM of numerators and LCM of denominators, then places LCM over LCM, instead of using LCM = LCM(numerators) / HCF(denominators).
The candidate overgeneralises the integer rule for LCM (which involves only one operation) and does not check with a simple example such as LCM(1/2, 1/3) = 1, which exposes the error.
What to do instead
Memorise the two fraction rules: LCM of fractions = LCM of numerators / HCF of denominators; HCF of fractions = HCF of numerators / LCM of denominators. Before answering, verify with a small numerical example (e.g., LCM of 2/3 and 3/4 is 6) to confirm the formula is applied correctly.
While computing successive percentage changes, the candidate adds or subtracts the percentages (e.g., a 20% increase followed by a 10% decrease is taken as a net 10% increase) rather than multiplying the factors (1.20 × 0.90 = 1.08, a net 8% increase).
Additive reasoning feels natural and is reinforced by everyday phrases like 'up 20 then down 10', and the candidate does not anchor the second percentage to the new base.
What to do instead
Always convert each percentage change to a multiplying factor and multiply factors in sequence. For two changes a% and b%, use net change = a + b + ab/100 (with signs). Drill with a quick sanity check: a 20% rise then 20% fall must give a net fall of 4%, not zero.
In profit and loss problems, the candidate computes profit percentage on the selling price instead of the cost price, or confuses marked price with cost price when a discount is also given.
The problem statement may present selling price first or use terms like 'marked price' and 'discount' together, and the candidate grabs the most recent number without identifying the base for the percentage.
What to do instead
Before calculating, write down explicitly: CP = ?, SP = ?, MP = ?, Discount = ?. Always compute profit% = (SP − CP)/CP × 100. For discount problems, first find SP = MP × (1 − d/100), then compare SP with CP. Practise 10 mixed problems where you label each quantity before solving.
When a discount of d% is offered on the marked price and then a further discount of e% is offered on the reduced price, the candidate adds the two discounts (d + e)% instead of applying them successively: effective discount = 1 − (1 − d/100)(1 − e/100).
The word 'discount' appears twice and the candidate treats them as additive, similar to the percentage-change error, without recognising that the second discount applies to a smaller base.
What to do instead
Treat successive discounts exactly like successive percentage decreases: multiply the remaining fractions. For 20% and 10%, effective discount = 1 − 0.8 × 0.9 = 28%, not 30%. Use the formula d + e − de/100 for two discounts and verify with a concrete CP of 100.
In partnership problems, the candidate splits profit in the ratio of capital contributions only, ignoring the different time periods for which each partner invested.
The word 'ratio' triggers the simple capital ratio, and the candidate overlooks the phrase 'invested for x months' or assumes all investments are for the same duration.
What to do instead
Always compute each partner's share as capital × time (in months or years, consistently). Profit ratio = C1×T1 : C2×T2 : … . If times are equal, it reduces to the capital ratio. Before solving, underline the time period for each partner and convert all to the same unit.
In time and work problems involving pipes and cisterns, the candidate adds the rates of an inlet and an outlet pipe instead of subtracting the outlet rate, or forgets that the outlet works against the filling.
The candidate applies the 'work together' formula (sum of rates) mechanically without checking the direction of each pipe; the outlet pipe's negative contribution is not explicitly represented.
What to do instead
Assign a positive sign to inlet pipes and a negative sign to outlet pipes before adding rates. Work with rates as fractions of the tank per hour: net rate = sum(inlet rates) − sum(outlet rates). If the net rate is negative, the tank never fills. Solve a few problems with one inlet and one outlet to build the habit.
In train problems, the candidate uses the train's speed to find the time to cross a platform but forgets to add the platform length to the train length, or uses the wrong relative speed when two trains move in the same direction.
The candidate focuses on the train alone and treats the platform as a point, or uses the sum of speeds for same-direction motion because 'relative speed' is remembered only as a sum.
What to do instead
Memorise: time to cross a platform = (length of train + length of platform) / speed of train. For two trains: opposite direction → relative speed = sum; same direction → relative speed = difference. Always convert speeds to m/s by multiplying by 5/18 when lengths are in metres. Sketch the situation before computing.
When computing a weighted average or alligation, the candidate takes the simple arithmetic mean of the quantities or prices instead of weighting by the quantities involved.
The candidate sees two or more numbers and automatically averages them, missing the words 'mixed in the ratio' or 'quantities are not equal'.
What to do instead
Use the alligation rule: ratio of quantities = (mean price − cheaper price) : (dearer price − mean price). Alternatively, compute total value / total quantity. Before solving, write down the weights explicitly. Test with an extreme case (e.g., 1 kg at ₹10 mixed with 100 kg at ₹20) to see that the simple mean is wrong.
In compound interest problems, the candidate applies simple interest for each year or uses the CI formula with the wrong number of compounding periods (e.g., uses annual rate for half-yearly compounding without adjusting rate and time).
The candidate memorises A = P(1 + r/100)^n but does not adjust r and n when compounding frequency changes, or confuses CI with SI when the period is not a whole number of years.
What to do instead
For compounding m times a year, use rate per period = r/m and number of periods = n×m. For fractional years, compute CI for full years and then simple interest on the amount for the remaining fraction. Always write the formula with substituted values before calculating, and check that CI > SI for the same P, r, n > 1.
In coding-decoding, the candidate identifies the pattern from one example and applies it to the target word without checking that the same rule holds for all given examples, or ignores letter positions from the end of the alphabet.
The candidate stops at the first plausible pattern (e.g., +1 shift) and does not verify consistency across all coded words, or forgets that A=1, Z=26 but reverse coding uses A=26, Z=1.
What to do instead
For every coding question, write the alphabet with positions 1–26 and also the reverse positions. Test the hypothesised rule on every given example before applying it. If two rules fit, check which one produces a unique answer. Practise 15 mixed coding questions and explicitly note the rule used.