Arithmetic Word Problems Cheat Sheet - IBPS PO (Probationary Officer) Prelims

1. Fundamental Translation Guide

Translating English word statements into precise algebraic equations is the foundational skill required for high accuracy in IBPS PO Prelims arithmetic. Below is the quick reference translation chart:

• Sum, Increased by, More than: Addition (\(+\))
• Difference, Decreased by, Less than: Subtraction (\(-\))
• Product, Of, Twice, Times: Multiplication (\(\times\))
• Quotient, Per, Ratio, Out of: Division (\(\div\))
• Is, Are, Equals, Results in: Equal sign (\(=\))

2. Percentage & Profit-Loss

Percentage Change Formula

\[\text{Percentage Change} = (\frac{\text{New Value} - \text{Old Value}}{\text{Old Value}}) \times 100\]

Successive Percentages

If a quantity changes successively by \(a\%\) and then by \(b\%\), the net percentage change is given by:

\[\text{Net Change} = (a + b + \frac{ab}{100})\%\]

Profit, Loss, and Discount Equations

• \(\text{Profit (P)} = \text{SP} - \text{CP}\) (when \(\text{SP} > \text{CP}\))
• \(\text{Loss (L)} = \text{CP} - \text{SP}\) (when \(\text{CP} > \text{SP}\))
• \(\text{Profit \%} = (\frac{\text{Profit}}{\text{CP}}) \times 100\)
• \(\text{Discount} = \text{Marked Price (MP)} - \text{SP}\)

3. Ratio, Proportion & Partnership

Direct & Inverse Proportion

• Direct Proportion: \(y = kx \implies \frac{y_1}{x_1} = \frac{y_2}{x_2}\)
• Inverse Proportion: \(y = \frac{k}{x} \implies x_1 y_1 = x_2 y_2\)

Partnership Rule

In partnership problems, profits are shared directly proportional to the product of capital invested and time period:

\[\text{Ratio of Profit} = (C_1 \times T_1) : (C_2 \times T_2) : (C_3 \times T_3)\]

4. Averages, Mixtures & Alligation

Average Concepts

\[\text{Average} = \frac{\text{Sum of Observations}}{\text{Number of Observations}}\]

Weighted Average:

\[\text{Avg}_{mix} = \frac{n_1 \bar{x}_1 + n_2 \bar{x}_2}{n_1 + n_2}\]

Rule of Alligation

To mix two ingredients of cost \(C_1\) and \(C_2\) (where \(C_1 < M < C_2\)) to obtain a mixture of mean cost \(M\):

\[\frac{\text{Quantity of Cheaper}}{\text{Quantity of Dearer}} = \frac{C_2 - M}{M - C_1}\]

5. IBPS PO Prelims PYQ Analysis & Weightage

In the Quantitative Aptitude section of the IBPS PO Prelims examination, Arithmetic Word Problems constitute approximately 10 to 15 questions out of 35. Mastering core topics such as Percentages, Profit & Loss, Ratio & Partnership, and Averages/Alligation is critical for clearing the cutoff. Past year pattern analysis indicates that candidates who utilize systematic word-to-math translation strategies achieve significantly higher accuracy within time limits.

6. Frequently Asked Questions (FAQ)