CBSE Linear Equations Subject Notes

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Linear Equations

11. A man has only 20 paisa coins and 25 paisa coins in his purse. If he has 50 coins in all totaling Rs 11.25, how many coins of each kind does she has?
12. The age of two girls are in the ratio 5:7 Eight years ago their ages were in the ratio 7:13. Find their present ages.
13. The taxi charges in a city comprise of a fixed charge together with the charge for the distance covered. For a journey of 10km, the charges paid are Rs 75 and for a journey of 15km, the charge paid are Rs 110. What will a person have to pay for travelling a distance of 25 km?
14. A man travels 600km partly by train and partly by car. If he covers 400km by train and the rest by car, it takes him 6 hours and 30 minutes. But if he travels 200 km by train and rest by car, he takes half an hour longer. Fine the speed of the train and that of the car.
15. The sum of a two digit number and the number obtained by reversing the order of its digits is 99. If the digits differ by 3, find the number.
16. Two years ago a father was five times as old as his son. Two years later, his age will be 8years more than three times the age of the son. Find the present ages of father and son.
17. The monthly incomes of A and B are in the ratio of 9:7 and their monthly expenditures are in the ratio of 4:3. If each saves Rs 1600per month, find the monthly incomes of each.
18. A number consisting of two digits is equal to 7 times the sum of its digits. When 27 is subtracted from the number, the digits interchange their places. Find the number.
19. The present age of a father is equal to the sum of the ages of his 5 children. 12 years hence the sum of the ages of his children will be twice the ages of their father. Find the present age of the father.
20. 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 6 hours and 30 minutes. But if he travels 200 km by train and rest by car, he takes half an hour longer. Find the speed of the train and that of car.
21. Two places A and B are 80 km apart from each other on a highway. A car stats from A and another 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 the meet in 1hour and 20 minutes. Find the seed of the cars.
22. A train covered a certain distance at a uniform speed. If the train would have 6 km/hr. faster it would have taken 8 hrs. less than the scheduled time. And if the train were slower by 6 km/hr. it would have taken 12 hours more than the scheduled time. Find the length of the journey.
23. A motorboat, whose speed is 9 km / hr in still water, goes 12 km downstream and comes back in a total time of 3 hrs. Find the speed of the stream.
24. For what values of 'p' and 'q', the following system of linear equations will have infinite number of solutions?

    2x - (p - 4)y = 2q + 1 4x - (p - 1)y = 5q - 1.

25. If twice the father's age is added to the son's age, the sum is 77. Five years ago, the father was 15 times the age of his son, then. Find their present ages.
26. Solve the following system of equations: 3 ( 2u + v) = 7 u v 3 ( u + 3 v) = 11 u v
27. The sum of a two-digit number and the number obtained by reversing the order of digits is 132. If 12 is added to the number, the new number becomes 5 times the sum of the digits. Find the number.
28. Solve graphically:

    x + y = 4, 3x - 2y = -3

    Shade the region bounded by the lines and x- axis. Write the vertices of and find its area.

29. A certain number of students planned a picnic. The budget for food was Rs 3600. But 15 of these students failed to go and thus the cost of food for each student increased by Rs 8. How many students attended the picnic?
30. An express train takes 4 hours less for a journey of 1200 km if its speed is increased by 15 km/hr from its usual speed. Find its usual speed.
31. Solve for x and y (by cross multiplication method):

    5mx + 6ny = 28 3mx + 4ny = 18.

32. Solve the equation by quadratic formula: 5x² - 16x + 3 = 0.
33. A man can row 40 km upstream and 24 km downstream in 7 hours. He can also row 32 km upstream and 36 km downstream in 7 hours. Find his speed of rowing in still water and the speed of the stream.