Simple Arithmetic Equations — Study Notes

Overview

Simple arithmetic equations form the backbone of problem-solving in the UPSSSC PET Elementary Arithmetic section. These questions test your ability to translate real-world scenarios into mathematical expressions and solve for unknown values. Typically, you'll encounter 3–5 direct questions on linear equations, plus several word problems that require equation-building skills.

Mastering this topic is crucial because it's not just a standalone section—equation-solving skills underpin percentage problems, age-related questions, time-distance scenarios, and mixture problems. The exam consistently features straightforward single-variable linear equations alongside word problems involving money, ages, consecutive numbers, and basic transactions. Students who can quickly identify the variable, set up the equation correctly, and solve systematically gain valuable marks and save time for tougher questions.

The key challenge isn't the mathematics itself—it's translating Hindi/English problem statements into correct equations and avoiding calculation errors under time pressure. Focus on recognizing common problem patterns and developing a systematic solving approach.

Key Concepts

• **Linear equation in one variable**: An equation of the form ax + b = c, where a, b, c are known numbers and x is the unknown. The highest power of the variable is 1.

• **Solving principle**: Whatever operation you perform on one side of the equation, perform the same on the other side to maintain equality. This includes adding, subtracting, multiplying, or dividing both sides by the same non-zero number.

• **Transposition method**: Moving terms from one side to the other by changing their sign. If +5 is on the left, it becomes –5 when moved to the right; if ×3 is with x, it becomes ÷3 when moved across the equals sign.

• **Word problem translation**: "Sum" means addition (+), "difference" means subtraction (–), "product" means multiplication (×), "quotient" means division (÷), "is/was/will be" translates to equals (=).

• **Consecutive numbers**: If first number is x, then next consecutive integers are x+1, x+2, etc. For consecutive even numbers: x, x+2, x+4. For consecutive odd numbers: x, x+2, x+4.

• **Age problems pattern**: If present age is x, then age after n years = x+n, and age n years ago = x–n.

• **Verification step**: Always substitute your answer back into the original equation or problem statement to check correctness—this catches arithmetic errors.

• **Unknown identification**: In word problems, identify what you need to find and assign it as your variable (x). Express all other quantities in terms of this variable.

Formulas / Key Facts

• **Basic linear equation**: ax + b = c → Solution: x = (c – b)/a

• **Equation with variable on both sides**: ax + b = cx + d → Collect like terms → (a – c)x = d – b → x = (d – b)/(a – c)