Algebra — RRB NTPC Mathematics
This topic carries roughly 8% of Mathematics's 30 questions. Nothing here goes beyond linear equations, simple factorable quadratics, and a handful of standard algebraic identities — the skill is setting up a word problem's equation correctly, not solving an already-given equation.
1. What RRB NTPC actually asks
Expect solving linear equations in one variable, simultaneous linear equations in two variables, factoring simple quadratics, applying standard algebraic identities, and age-based word problems that translate into linear equations.
2. Standard algebraic identities
| Identity | Formula |
|---|---|
| Square of a sum | (a+b)² = a² + 2ab + b² |
| Square of a difference | (a−b)² = a² − 2ab + b² |
| Difference of squares | a² − b² = (a+b)(a−b) |
| Sum/difference derived | a² + b² = (a+b)² − 2ab, also = (a−b)² + 2ab |
These identities let you find a² + b² (or similar combined expressions) directly from a+b and ab, without solving for a and b individually first — a significant time-saver.
3. Solving simultaneous equations
For two linear equations in two variables, use either substitution (solve one equation for one variable, substitute into the other) or elimination (multiply equations to match coefficients, then add or subtract to eliminate one variable). Elimination is usually faster when coefficients align easily.
4. Age-based word problems
The standard setup: assign a variable to each person's current age, translate every stated relationship (ratio, sum, "after N years") into an equation, then solve the resulting system. The key discipline is translating "after N years" correctly — both people's ages increase by N, not just one.
Worked examples
Q1. If a + b = 10 and ab = 21, what is a² + b²?
Pick an option to check your answer.
Show explanation
Solution. Using the identity a² + b² = (a+b)² − 2ab: a² + b² = 10² − 2(21) = 100 − 42 = 58.
This avoids solving for a and b individually (which would require factoring a quadratic first) — the identity gets to the answer in one step. Answer: (c).
Q2. A father's age is 3 times his son's age. After 12 years, the father's age will be twice the son's age. What is the father's present age?
Pick an option to check your answer.
Show explanation
Solution. Let the son's present age = s, so the father's present age = 3s. After 12 years: father's age = 3s+12, son's age = s+12. The condition states 3s+12 = 2(s+12).
Solving: 3s + 12 = 2s + 24, so s = 12. Father's present age = 3 × 12 = 36. Verify: after 12 years, father = 48, son = 24, and 48 is indeed twice 24. Answer: (c).
6. Common traps
- Forgetting to add N to BOTH people's ages in an "after N years" condition — both people age together, not just one.
- Solving for individual variables when an identity would answer the question directly. If only a combined expression like a²+b² or a²−b² is asked, use the identity instead of fully solving for a and b.
- Sign errors in (a−b)² expansion. The middle term is −2ab, not +2ab — easy to drop the sign under time pressure.
- Mis-setting-up ratio-based age problems. "A's age is 3 times B's age" means A = 3B, not B = 3A — read the sentence direction carefully.
7. Guessing strategy
For age problems, a quick sanity check (does the "after N years" condition hold true for the candidate answer?) is a fast, reliable way to verify or eliminate an option without re-solving from scratch.
Summary
- Algebra is roughly 8% of Mathematics's 30 CBT 1 questions, staying at a basic (linear equations, simple quadratics, identities) level.
- Memorise (a+b)², (a−b)², and a²−b²=(a+b)(a−b) cold — they answer "combined expression" questions in one step.
- For simultaneous equations, use elimination when coefficients align easily, substitution otherwise.
- In "after N years" word problems, both people's ages increase by N — a frequent source of setup errors.
- Read ratio-based sentences carefully for direction: "A is 3 times B" means A = 3B, not the reverse.
- Verifying a candidate answer against the original word-problem condition is often faster than re-solving from scratch.
