RBI Assistant Numerical Ability (Quantitative Aptitude) Syllabus

What is the formula for Simple Interest, and for Amount?

Simple Interest (SI) = (P × R × T)/100, where P=principal, R=rate% per annum, T=time in years. Amount = P + SI = P(1 + RT/100).

What is the formula for Compound Interest (compounded annually)?

Amount = P(1 + R/100)^T. Compound Interest = Amount − P = P[(1 + R/100)^T − 1].

What is the difference between CI and SI for 2 years on the same principal and rate?

Difference (2 years) = P(R/100)². For 3 years, difference = P(R/100)²(3 + R/100) = P(R²(300+R))/100³.

How is compound interest calculated when compounded half-yearly or quarterly?

Half-yearly: rate becomes R/2 and time becomes 2T, so A = P(1 + R/200)^(2T). Quarterly: A = P(1 + R/400)^(4T).

What is the basic relationship between speed, distance, and time?

Speed = Distance/Time; Distance = Speed × Time; Time = Distance/Speed. Speed is inversely proportional to time for a fixed distance.

How do you convert between km/h and m/s?

To convert km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5.

What is the average speed for equal distances covered at speeds x and y?

Average speed = 2xy/(x+y) (the harmonic mean), used when equal distances are traveled at different speeds.

In trains/relative speed problems, how is relative speed found for same and opposite directions?

Same direction: relative speed = difference of speeds (s1 − s2). Opposite direction: relative speed = sum of speeds (s1 + s2). Time to cross = total length/relative speed.

In Time and Work, if A can do a job in n days, what is A's one-day work, and how do you combine workers?

A's one day work = 1/n. If A does 1/a per day and B does 1/b per day, together they do (1/a + 1/b) per day, finishing in ab/(a+b) days.

What is the relationship between number of workers, days, and work done (M1D1/W1 = M2D2/W2)?

M1×D1×H1/W1 = M2×D2×H2/W2, where M=men, D=days, H=hours/day, W=work. Used for comparing two work scenarios.

In pipes and cisterns, how do inlet and outlet pipes combine?

An inlet pipe filling in x hours contributes +1/x per hour; an outlet pipe emptying in y hours contributes −1/y per hour. Net rate = (1/x − 1/y) per hour.

What is the rule of alligation, and what does it find?

Alligation finds the ratio in which two ingredients at different prices/concentrations are mixed to get a desired mean. Ratio = (Dearer value − Mean)/(Mean − Cheaper value), giving Cheaper:Dearer.

In a mixture, after replacing part of it repeatedly, what is the remaining quantity of the original liquid?

After n replacements, remaining original = Initial × (1 − x/V)^n, where x is the amount replaced each time and V is the total volume.

In Tabular Data Interpretation, what is the standard approach to solving questions?

Read the table title, row/column headings and units carefully; identify exactly which cells the question needs; extract values, then apply the operation (totals, averages, ratios, percentage change) only on the relevant data.

In a Bar Graph, what does each bar represent and how is percentage change between two bars found?

Each bar's height/length represents a value for a category or time period. Percentage change = [(later value − earlier value)/earlier value] × 100.

How is a Line Graph read and what is it best suited for?

A line graph plots data points connected by lines over a continuous variable (usually time). It is best for showing trends, increases/decreases, and comparing multiple series over the same period.

In a Pie Chart, how do you convert between percentages, degrees, and actual values?

Whole circle = 360° = 100% = total value. Degrees = (percentage/100)×360. Value of a sector = (sector% /100) × total. Percentage = (sector angle/360)×100.

In a Caselet DI, what is the key first step before answering?

Convert the paragraph of text into structured data (a table, equations, or a Venn diagram) by extracting all numbers and relationships, then solve the questions from that structured form.

In Mixed DI, what should a student watch for compared to single-source DI?

Mixed DI combines two or more chart/table types (e.g., table + pie). Watch for shared totals across sources, different units, and questions requiring data from more than one chart simultaneously.

In Number Series, what are the common patterns to check?

Check for: constant difference (arithmetic), constant ratio (geometric), differences of differences, squares/cubes, prime numbers, alternating series, and combined operations (×, +, then repeat).

How do you find the missing or wrong term in a number series?

Identify the rule from consecutive terms (difference, ratio, or pattern of operations), apply it consistently, and find the term that breaks the rule (wrong) or fill the gap using the rule (missing).

What is the standard form of a quadratic equation and the quadratic formula?

Standard form: ax² + bx + c = 0 (a≠0). Roots x = [−b ± √(b²−4ac)]/(2a).

For a quadratic ax²+bx+c=0, what is the sum and product of roots?

Sum of roots = −b/a; Product of roots = c/a.

What does the discriminant (D = b²−4ac) tell you about the nature of quadratic roots?

If D>0: two distinct real roots. If D=0: two equal real roots. If D<0: no real roots (complex/imaginary roots).

In quadratic comparison questions, how do you decide the relationship between x and y?

Solve both equations for their roots, then compare every value of x with every value of y. Conclude x>y, x<y, x≥y, x≤y, x=y, or 'no relation' based on whether the comparison holds for all combinations.

What are the formulas for permutations nPr and combinations nCr?

nPr = n!/(n−r)! (arrangements where order matters). nCr = n!/[r!(n−r)!] (selections where order does not matter). Relation: nPr = nCr × r!.

What is the basic formula for probability, and the range of probability values?

Probability = (Number of favorable outcomes)/(Total number of outcomes). Probability always lies between 0 and 1 inclusive. P(not E) = 1 − P(E).

What are the area and perimeter formulas for a rectangle, square, triangle, and circle?

Rectangle: area = l×b, perimeter = 2(l+b). Square: area = a², perimeter = 4a. Triangle: area = ½×base×height. Circle: area = πr², circumference = 2πr.

What are the volume and surface area formulas for a cube, cuboid, cylinder, and sphere?

Cube: V = a³, TSA = 6a². Cuboid: V = l×b×h, TSA = 2(lb+bh+hl). Cylinder: V = πr²h, CSA = 2πrh. Sphere: V = (4/3)πr³, surface area = 4πr².

In Data Sufficiency, what do the standard answer options I, II, both, either, or neither mean?

Determine if statement I alone is sufficient, II alone is sufficient, both together are needed, either alone suffices, or neither is sufficient. Decide sufficiency without actually solving fully; do not assume facts beyond the statements.