NCERT Class 10 Maths — Chapter 3

Exercise 3.5: Cross-Multiplication and Word Problems

A mix of cross-multiplication technique and word problems involving ages, speeds, fractions, and money. This exercise tests whether you can set up equations from real situations.

cross-multiplication methodword problemsage problemsspeed-distance-time
4
NCERT Questions
10
Practice MCQs
4
Key Concepts
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Extra Practice Questions

These questions cover the same concepts as Exercise 3.5. Try solving them to build confidence before or after the textbook exercise.

1

For what value of 'k' will the following pair of linear equations have no solution? 3x + y = 1 (2k - 1)x + (k - 1)y = 2k + 1

A.k = 0
B.k = 1
C.k = 2
D.k = -1
2

The cost of 5 pens and 7 notebooks is ₹255, while the cost of 7 pens and 5 notebooks is ₹249. What is the cost of one pen and one notebook, respectively?

A.₹20, ₹25
B.₹22, ₹21
C.₹25, ₹20
D.₹21, ₹22
3

For the pair of linear equations: ax + by + c = 0 dx + ey + f = 0 Which of the following statements correctly represents the setup for finding 'x' using the cross-multiplication method?

A.x / (bf - ce) = 1 / (ae - bd)
B.x / (be - cf) = 1 / (af - cd)
C.x / (bf - ce) = y / (cd - af)
D.x / (ae - bd) = 1 / (bf - ce)
4

For which value of 'k' will the pair of linear equations 3x + y = 1 and (2k - 1)x + (k - 1)y = 2k + 1 have no solution?

A.k = 1
B.k = 2
C.k = -1
D.k = 0
5

For a pair of linear equations in two variables, (x, y) = (p, q) is a solution if:

A.It satisfies the first equation only.
B.It satisfies the second equation only.
C.It satisfies both equations simultaneously.
D.It is a point on the x-axis.
6

A point (a, b) is considered a solution to a pair of linear equations if:

A.it satisfies only the first equation.
B.it satisfies only the second equation.
C.it satisfies both equations simultaneously.
D.it is the midpoint of the line segments representing the equations.
7

For which value of 'p' will the following pair of linear equations have infinitely many solutions? px + 3y - (p - 3) = 0 12x + py - p = 0

A.p = 3
B.p = -6
C.p = 6
D.p = 0
8

Consider the system of linear equations a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0. Which of the following statements must be true if a1b2 - a2b1 = 0 and b1c2 - b2c1 = 0?

A.The system has a unique solution.
B.The system has no solution.
C.The system has infinitely many solutions.
D.The system is inconsistent.
9

Find the value of 'm' for which the pair of linear equations mx + y = 1 and (m² + 1)x + (m - 1)y = m has no solution.

A.m = 1
B.m = -1
C.m = 2
D.m = 0
10

Consider the pair of equations: Equation (1): x - 2y = 4 Equation (2): 3x + y = 5 Which method would be the most efficient to solve this particular system of equations and why?

A.Substitution method, because 'y' in Equation (2) can be easily isolated.
B.Elimination method, because the coefficients of 'x' are already multiples of each other.
C.Cross-multiplication method, because it is always the fastest method for any system.
D.Graphical method, because it always gives the exact solution quickly.

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Common Mistakes to Avoid

  • Setting up equations incorrectly from word problems
  • Forgetting units in the final answer
  • Not checking the solution makes sense in the real-world context

Other Exercises in Chapter 3

Frequently Asked Questions

How many questions are in Exercise 3.5?

Exercise 3.5 has 4 questions combining cross-multiplication with real-world word problems.

Is Exercise 3.5 important for boards?

Yes — word problems from this exercise are regularly asked for 3-4 marks in CBSE board papers.

Want to practise on paper? Download a free worksheet for this topic.

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