Word problems on linear pairs: Class 10 practice
Turn the story into two equations in two unknowns, then solve by substitution or elimination. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Solving a pair of equations
The idea behind word problems on linear pairs
Turn the story into two equations in two unknowns, then solve by substitution or elimination. Typical stories: prices of two items, ages, fractions, digits.
Step-by-step method
- Name the two unknowns.
- Write two equations from the facts.
- Solve and check both conditions.
Worked example 1 (Basic)
4 pens and 1 pencils cost ₹200; 4 pens and 2 pencils cost ₹216. Find the cost of one pen and one pencil.
- 4p + 1q = 200
- 4p + 2q = 216
- p = ₹46, q = ₹16
- Answer: Pen ₹46, pencil ₹16
Worked example 2 (Standard)
2 pens and 1 pencils cost ₹32; 1 pens and 4 pencils cost ₹37. Find the cost of one pen and one pencil.
- 2p + 1q = 32
- 1p + 4q = 37
- p = ₹13, q = ₹6
- Answer: Pen ₹13, pencil ₹6
Worked example 3 (Challenge)
Two numbers add to 19 and differ by 5. Find them.
- a + b = 19, a − b = 5
- Answer: 12 and 7
Common mistakes and misconceptions
- Writing only one equation
- Answering with x when the question asks for both
Practice questions
- (Basic) 2 pens and 3 pencils cost ₹94; 1 pens and 1 pencils cost ₹33. Find the cost of one pen and one pencil.
- (Basic) Two numbers add to 81 and differ by 9. Find them.
- (Standard) 5 pens and 2 pencils cost ₹81; 2 pens and 2 pencils cost ₹54. Find the cost of one pen and one pencil.
- (Standard) 1 pens and 4 pencils cost ₹152; 5 pens and 3 pencils cost ₹284. Find the cost of one pen and one pencil.
- (Challenge) 5 pens and 4 pencils cost ₹312; 4 pens and 5 pencils cost ₹318. Find the cost of one pen and one pencil.
- (Challenge) 1 pens and 5 pencils cost ₹56; 3 pens and 3 pencils cost ₹60. Find the cost of one pen and one pencil.
Answer key with full working
- Q1: 2p + 3q = 94 → 1p + 1q = 33 → p = ₹5, q = ₹28 → Answer: Pen ₹5, pencil ₹28
- Q2: a + b = 81, a − b = 9 → Answer: 45 and 36
- Q3: 5p + 2q = 81 → 2p + 2q = 54 → p = ₹9, q = ₹18 → Answer: Pen ₹9, pencil ₹18
- Q4: 1p + 4q = 152 → 5p + 3q = 284 → p = ₹40, q = ₹28 → Answer: Pen ₹40, pencil ₹28
- Q5: 5p + 4q = 312 → 4p + 5q = 318 → p = ₹32, q = ₹38 → Answer: Pen ₹32, pencil ₹38
- Q6: 1p + 5q = 56 → 3p + 3q = 60 → p = ₹11, q = ₹9 → Answer: Pen ₹11, pencil ₹9
Syllabus note
This skill is listed under "Pair of Linear 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 word problems on linear pairs in?
"Pair of Linear 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.