Class 10 Maths Chapter 3 – Pair of Linear Equations Word Problems | USP Indore

Class 10 Maths Chapter 3 – Pair of Linear Equations in Two Variables: Word Problems

This page provides a comprehensive set of 15 word problems on Pair of Linear Equations in Two Variables for Class 10 Maths (Chapter 3), prepared by Unique Study Point (USP), Indore. All problems are based on the CBSE NCERT syllabus 2026-27 and are arranged category-wise for easy practice and revision.

Categories of Word Problems Covered

• 🎂 Age-Based Problems – 3 questions
• 🚂 Speed, Distance and Time Problems – 3 questions (including boat and stream)
• 📐 Geometry-Based Problems – 3 questions (rectangle, triangle, perimeter)
• 💰 Money and Coins Problems – 2 questions
• 🧪 Mixture Problems – 2 questions
• ⭐ Miscellaneous / Real-Life Problems – 2 questions (digits, marks)

Word Problems List (Q1 to Q15)

Q1 (Age). The sum of the ages of a father and his son is 45 years. Five years ago, the father\'s age was four times the age of the son. Find their present ages.

Q2 (Age). The present age of a woman is 3 times the present age of her daughter. After 12 years, she will be twice as old as her daughter. Find their present ages.

Q3 (Age). Seven years ago, Asha was five times as old as Nisha. Seven years hence, she will be twice as old. Find their present ages.

Q4 (Speed). A train travels 360 km at uniform speed. If the speed had been 5 km/hr more, it would have taken 1 hour less. Find the speed of the train and time taken.

Q5 (Boat & Stream). A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours it goes 40 km upstream and 55 km downstream. Find the speed of the boat in still water and the speed of the stream.

Q6 (Boat & Stream). Ritu can row downstream 20 km in 2 hours and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.

Q7 (Geometry). The perimeter of a rectangle is 44 cm. If the length is increased by 4 cm and the breadth is decreased by 2 cm, the area remains the same. Find the dimensions of the rectangle.

Q8 (Geometry). The angles of a triangle are x, y, and 45°. If the difference of the two unknown angles is 15°, find the value of x and y.

Q9 (Geometry). In a rectangle, if the length is reduced by 5 cm and the breadth is increased by 3 cm, it becomes a square. Also, the perimeter of this square is 4 cm less than the perimeter of the rectangle. Find its dimensions.

Q10 (Money). A bag contains ₹5 and ₹10 coins. If the total number of coins is 30 and the total amount is ₹200, find the number of coins of each type.

Q11 (Money). The cost of 5 oranges and 3 apples is ₹35 and the cost of 2 oranges and 4 apples is ₹28. Find the cost of each.

Q12 (Mixture). A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to get 80 litres of 6% solution. Find how many litres of each solution should be mixed.

Q13 (Mixture/Money). One says, \"Give me hundred, friend! I shall then become twice as rich as you.\" The other replies, \"If you give me ten, I shall be six times as rich as you.\" Find the amount each person has.

Q14 (Miscellaneous). In a class test, the sum of marks obtained by Ravi in Mathematics and Science is 28. Had he got 3 more marks in Mathematics and 4 less in Science, the product of marks would have been 180. Find the marks in each subject.

Q15 (Digits). The sum of the digits of a two-digit number is 9. If the digits are reversed, the number is increased by 27. Find the number.

How to Solve Pair of Linear Equations Word Problems – Tips

• Step 1: Read the problem carefully and identify the two unknown quantities.
• Step 2: Assign variables – let the unknowns be x and y.
• Step 3: Form two equations based on the given conditions.
• Step 4: Solve using Substitution, Elimination, or Cross-Multiplication method.
• Step 5: Verify your answer by substituting back into both equations.

Important FAQs on Linear Equations Word Problems

Q. Which method is best for solving word problems on linear equations?
Ans. The Elimination Method is usually fastest for speed-distance and mixture problems. Substitution Method works well for age and money problems where one variable can be easily expressed in terms of the other.

Q. What types of word problems come in CBSE Class 10 Maths Chapter 3 exam?
Ans. CBSE Class 10 exams regularly feature age problems, boat and stream problems, geometry problems (rectangle/triangle), money and coins problems, and digit-based problems from Chapter 3.

Q. How many marks do word problems carry in Class 10 Maths board exam?
Ans. Word problems from Pair of Linear Equations typically appear as 3-mark or 5-mark questions in the CBSE Class 10 Maths board examination.

Q. What is the difference between upstream and downstream speed?
Ans. If speed of boat in still water = u and speed of stream = v, then: Downstream speed = u + v, Upstream speed = u − v.

About Unique Study Point (USP), Indore

Unique Study Point (USP) is a leading coaching institute in Indore, Madhya Pradesh, providing quality education for Classes VI to X in Mathematics, Science, and Social Science. All study materials follow the latest CBSE-NCERT syllabus and are designed for effective exam preparation.

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