Important Extra Questions for Class 10 Maths – Linear Equations in Two Variables (CBSE)

🧮 Important Extra Questions for Class 10 Maths – Linear Equations in Two Variables (CBSE)

Are you preparing for your Class 10 CBSE Board Exams and looking for extra practice questions from the chapter Linear Equations in Two Variables?
Here’s a curated set of challenging and exam-relevant problems from NCERT, CBSE Board Papers, and Exemplar sources.
These questions are perfect for revision, homework, and board exam preparation, especially for students aiming for full marks in the Algebra section.

📘 Solve these step by step and strengthen your understanding of linear equations involving speed, distance, and time problems.

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Extra Questions – Linear Equations in Two Variables (CBSE Class 10 Maths)

4. A boat goes 24 km upstream and 28 km downstream in 6 hrs. It goes 30 km upstream and 21 km downstream in 6 ½ hrs. Find the speed of the boat in still water and also speed of the stream.

5. A man walks a certain distance with certain speed. If he walks ½ km an hour faster, he takes 1 hour less. But, if he walks 1 km an hour slower, he takes 3 more hours. Find the distance covered by the man and his original rate of walking.

6. A person rowing at the rate of 5 km/h in still water, takes thrice as much time in going 40 km upstream as in going 40 km downstream. Find the speed of the stream.

7. Ramesh travels 760 km to his home partly by train and partly by car. He takes 8 hours if he travels 160 km by train and the rest by car. He takes 12 minutes more if he travels 240 km by train and the rest by car. Find the speed of the train and car respectively.
(NCERT EXEMPLAR)

8. A man travels 600 km partly by train and partly by car. If he covers 400 km by train and the rest by car, it takes him 6 hours and 30 minutes. But, if he travels 200 km by train and the rest by car, he takes half an hour longer. Find the speed of the train and that of the car.
(CBSE 2001)

9. Places A and B are 80 km apart from each other on a highway. A car starts from A and other from B at the same time. If they move in the same direction, they meet in 8 hours and if they move in opposite directions, they meet in 1 hour and 20 minutes. Find the speeds of the cars.
(CBSE 2002)

10. A boat goes 12 km upstream and 40 km downstream in 8 hours. It can go 16 km upstream and 32 km downstream in the same time. Find the speed of the boat in still water and the speed of the stream.

11. Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.

12. 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.
(NCERT)

13. A motor boat can travel 30 km upstream and 28 km downstream in 7 hours. It can travel 21 km upstream and return in 5 hours. Find the speed of the boat in still water and the speed of the stream.
(NCERT EXEMPLAR)

14. Abdul travelled 300 km by train and 200 km by taxi, it took him 5 hours 30 minutes. But if he travels 260 km by train and 240 km by taxi he takes 6 minutes longer. Find the speed of the train and that of the taxi.

15. A train covered a certain distance at a uniform speed. If the train could have been 10 km/hr. faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10 km/hr; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train.
(CBSE 2006C)

🏁 Tips for Students:

• Practice forming two linear equations using the given conditions.

• Solve them using substitution or elimination methods.

• Cross-check your answers by substituting values.