BCS Written Math & Mental Ability study guide
BCS Written Math & Mental Ability · Work through your exam, one topic at a time.
The BCS Written Math & Mental Ability component is the quantitative and reasoning portion of Bangladesh's Bangladesh Civil Service (BCS) examination, the competitive recruitment process for cadre and non-cadre government posts. It is intended for graduates preparing for public-service careers, and it rewards candidates who can compute quickly and accurately under pressure as much as those who know advanced mathematics. The BCS Written Math & Mental Ability study guide has 10 sections and about 4,044 words.
01Arithmetic: Number Systems, HCF/LCM, Fractions and Decimals
Start with divisibility rules (2,3,4,5,6,8,9,11), prime factorisation, and the classification of numbers (natural, integer, rational, irrational). Every HCF/LCM question becomes easy once you factorise: HCF takes the lowest power of common primes, LCM takes the highest power of all primes.
324 words, about 2 min02Percentage
A percentage is a fraction with denominator 100. Convert freely: 37.5% = 3/8, 16⅔% = 1/6, 62.5% = 5/8, 12.5% = 1/8.
291 words, about 1 min03Profit and Loss
Establish the vocabulary: cost price (CP), selling price (SP), marked price (MP). Profit = SP − CP when SP CP; loss is the reverse.
327 words, about 2 min04Discount
Marked price (MP) is the list price; discount is a reduction on MP, so discount% = (MP − SP)/MP × 100. This is the key structural distinction from profit and loss: discount lives on MP, profit lives on CP .
316 words, about 2 min05Ratio, Proportion and Partnership
A ratio a:b compares like quantities and is scale-free; a proportion a:b = c:d states equality of two ratios, with the cross-product rule ad = bc. Learn the derived rules: if a/b = c/d, then each equals (a+c)/(b+d) (componendo), and invertendo, alternando, and dividendo follow from it.
312 words, about 2 min06Time, Work and Pipes/Cisterns
The central idea is rate: if A finishes a job in n days, A's one-day work is 1/n. Combined rates add: together they take 1/(1/a + 1/b) days.
302 words, about 2 min07Speed, Time, Distance and Trains
The foundation is Distance = Speed × Time, with unit consistency: 1 km/h = 5/18 m/s, and 1 m/s = 18/5 km/h. Average speed is total distance ÷ total time, not the arithmetic mean of the speeds, unless the distances are equal - in which case the average is 2xy/(x+y).
301 words, about 2 min08Average
Average (arithmetic mean) = sum of observations ÷ number of observations. Rearranged, sum = average × count, which is the workhorse of most exam questions.
309 words, about 2 min09Mixture and Alligation
Alligation is a shortcut for combining two ingredients of different values. Arrange the cheaper price and the dearer price in a column, put the mean price in the middle, and cross-subtract: the ratio of quantities is (dearer − mean) : (mean − cheaper).
308 words, about 2 min10Interest: Simple and Compound
Simple interest is SI = P × R × T / 100, where P is principal, R the annual rate, and T the time in years. It grows linearly, so doubling the time doubles the interest.
1,254 words, about 6 min