IBPS SO Quantitative Aptitude (Numerical Ability) Syllabus

What is discount, and on which price is it calculated?

Discount is a reduction on the Marked Price (MP). Discount% = (Discount/MP) × 100; SP = MP × (100 − Discount%)/100.

How do you find net effect of two successive discounts of a% and b%?

Net discount = a + b − (ab/100) percent. E.g., 10% then 20% = 28% overall discount.

State the Simple Interest formula.

SI = (P × R × T)/100, where P = principal, R = rate% per annum, T = time in years. Amount = P + SI.

State the Compound Interest amount formula (annual compounding).

A = P(1 + R/100)ᵀ; CI = A − P.

For CI compounded n times a year, what is the amount formula?

A = P(1 + R/(100n))^(nT). For half-yearly, rate halves and time doubles.

What is the difference between CI and SI for 2 years at rate R?

Difference = P × (R/100)². For 2 years it equals P·R²/10000.

State the basic relation between speed, distance and time.

Speed = Distance/Time; Distance = Speed × Time; Time = Distance/Speed.

How do you convert km/hr to m/s and vice versa?

km/hr to m/s: multiply by 5/18. m/s to km/hr: multiply by 18/5.

Time taken for a train of length L to cross a stationary pole vs a platform of length P?

Pole: L/speed. Platform: (L + P)/speed (must cover its own length plus the platform).

Relative speed of two trains moving in same vs opposite directions?

Same direction: subtract speeds (v₁ − v₂). Opposite direction: add speeds (v₁ + v₂).

If A does work in 'a' days and B in 'b' days, time taken together?

Together = (a × b)/(a + b) days; combined one-day work = 1/a + 1/b.

A pipe fills a tank in x hours; an outlet empties it in y hours. Net time to fill if both open?

Net fill rate = 1/x − 1/y per hour; time = xy/(y − x) hours (only fills if x < y).

State the alligation rule for mixing two ingredients.

(Quantity cheaper)/(Quantity dearer) = (Dearer price − Mean price)/(Mean price − Cheaper price).

In partnership, how is profit shared when capitals and times differ?

Profit is divided in the ratio of (Capital × Time) for each partner.

A vessel has milk-water in ratio; replace part with water repeatedly. Milk left after n replacements?

Milk left = Initial × (1 − replaced/total)ⁿ. This is the classic milk-water replacement formula.

State the average formula and effect of adding/removing a value.

Average = Sum of observations / Number of observations. Adding a value above the average raises it; below lowers it.

How do you handle 'average of consecutive numbers'?

Average of consecutive (or evenly spaced) numbers = (first + last)/2, equal to the middle term.

State age problem basics: present age x, how to express 'n years ago' and 'after n years'.

n years ago: (x − n). After n years: (x + n). Set up equations from ratio/sum conditions given.

Give mensuration formulas for area of rectangle, triangle, and circle.

Rectangle = l × b; Triangle = ½ × base × height; Circle = πr².

Give volume formulas for cube, cuboid, cylinder, and sphere.

Cube = a³; Cuboid = l×b×h; Cylinder = πr²h; Sphere = (4/3)πr³.

In Tabular DI, what is the first step before answering questions?

Read row/column headers and units carefully, note totals given, and identify what each cell represents to avoid misreading data.

In a Line/Bar Graph DI, how do you compute percentage increase between two years?

% increase = ((Later value − Earlier value)/Earlier value) × 100. Read values precisely from the axis scale.

In a Pie Chart, how do you convert a sector's degrees or percentage into a value?

Value = (sector% × total) or (sector degrees/360 × total). 1% = 3.6°, so degrees = % × 3.6.

What characterizes a Caselet (Mixed) DI question?

Data is given as a paragraph of text (no chart/table); you must extract numbers, often build your own table, then solve.

In Missing Data DI, how do you find an unknown cell?

Use given totals, ratios, or relationships (e.g., row/column totals, percentages) stated in the problem to back-calculate the missing value.

In Quantity Comparison DI, what are the typical answer options?

Compute Quantity I and Quantity II, then choose: I>II, I<II, I≥II, I≤II, or I=II / no relation. Compare the two derived quantities.

What is asked in a Data Sufficiency question (not the answer itself)?

Whether the given statements are SUFFICIENT to answer the question — using Statement I alone, II alone, either, both together, or neither. You do not compute the final value.

State the formulas for permutation (nPr) and combination (nCr).

nPr = n!/(n−r)! (order matters); nCr = n!/(r!(n−r)!) (order does not matter).

State the basic probability formula and its range.

P(E) = (Favorable outcomes)/(Total outcomes); 0 ≤ P(E) ≤ 1. P(not E) = 1 − P(E).

For a quadratic ax²+bx+c=0, give the sum and product of roots, and how to compare two roots' equations.

Sum of roots = −b/a; Product = c/a. To solve, factor or use x = [−b ± √(b²−4ac)]/2a, then compare the two roots with the other equation's roots.