Quadratic equation word problems: Class 10 practice
Many problems about areas, consecutive numbers or speeds lead to a quadratic. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Solving quadratic equations
The idea behind quadratic equation word problems
Many problems about areas, consecutive numbers or speeds lead to a quadratic. Set up the equation, solve it, and reject any root that doesn't fit the situation (like a negative length).
Step-by-step method
- Name the unknown.
- Write the equation and bring it to ax² + bx + c = 0.
- Solve by factorising or the formula.
- Keep only sensible roots and check.
Worked example 1 (Basic)
The product of two consecutive positive integers is 30. Find them.
- x(x + 1) = 30
- x² + x − 30 = 0 → (x − 5)(x + 6) = 0
- x = 5 (reject −6)
- Answer: 5 and 6
Worked example 2 (Standard)
A rectangle's length is 5 m more than its width, and its area is 414 m². Find its dimensions.
- x(x + 5) = 414
- x² + 5x − 414 = 0 → x = 18 (reject −23)
- Answer: 18 m by 23 m
Worked example 3 (Challenge)
A rectangle's length is 5 m more than its width, and its area is 456 m². Find its dimensions.
- x(x + 5) = 456
- x² + 5x − 456 = 0 → x = 19 (reject −24)
- Answer: 19 m by 24 m
Common mistakes and misconceptions
- Keeping a negative length
- Forgetting to answer the question asked
Practice questions
- (Basic) The product of two consecutive positive integers is 156. Find them.
- (Basic) The product of two consecutive positive integers is 132. Find them.
- (Standard) A rectangle's length is 4 m more than its width, and its area is 357 m². Find its dimensions.
- (Standard) A rectangle's length is 5 m more than its width, and its area is 266 m². Find its dimensions.
- (Challenge) A rectangle's length is 7 m more than its width, and its area is 228 m². Find its dimensions.
- (Challenge) A rectangle's length is 9 m more than its width, and its area is 220 m². Find its dimensions.
Answer key with full working
- Q1: x(x + 1) = 156 → x² + x − 156 = 0 → (x − 12)(x + 13) = 0 → x = 12 (reject −13) → Answer: 12 and 13
- Q2: x(x + 1) = 132 → x² + x − 132 = 0 → (x − 11)(x + 12) = 0 → x = 11 (reject −12) → Answer: 11 and 12
- Q3: x(x + 4) = 357 → x² + 4x − 357 = 0 → x = 17 (reject −21) → Answer: 17 m by 21 m
- Q4: x(x + 5) = 266 → x² + 5x − 266 = 0 → x = 14 (reject −19) → Answer: 14 m by 19 m
- Q5: x(x + 7) = 228 → x² + 7x − 228 = 0 → x = 12 (reject −19) → Answer: 12 m by 19 m
- Q6: x(x + 9) = 220 → x² + 9x − 220 = 0 → x = 11 (reject −20) → Answer: 11 m by 20 m
Syllabus note
This skill is listed under "Quadratic Equations" for Class 10 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is quadratic equation word problems in?
"Quadratic Equations", Class 10 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.