Maths Questions on Linear Equations for Class 8

A student need to practice maths problems. Its helps in developing problem solving skills. The problems shall not be (i) too simple, (ii) too difficult or (iii) too many. Simple problems are boring, difficult problems discourages (at times), and too many problems don't leave time for fun.

I selected following problems on linear equations for my son studying in class 8.

1. Twenty-four is divided into two parts such that 7 times the first part added to 5 times the second part makes 146. Find each part.
2. The sum of the digits of a two-digit number is 12. If the new number formed by reversing the digits is greater than the original number by 54, find the original number.
3. The denominator of a rational number is greater than its numerator by 3. If 3 is subtracted from the numerator and 2 is added to its denominator, the new number becomes 1/5. Find the original number.
4. The length of a rectangle exceeds its breadth by 7 cm. If the length is decreased by 4 cm and the breadth is increased by 3 cm, the area of the new rectangle is the same as the area of the original rectangle. Find the length and the breadth of the original rectangle.
5. An altitude of a triangle is five-thirds the length of its corresponding base. If the altitude be increased by 4 cm and the base decreased by 2 cm, the area of the triangle remains the same. Find the base and the altitude of the triangle.
6. Two angles of a triangle are in the ratio 4:5. If the sum of these angles is equal to the third angle, find the angles of the triangle.
7. A boat goes downstream from one port to another in 9 hours. It covers the same distance upstream in 10 hours. If the speed of the stream be 1 km/hr, find the speed of the boat in still water and the distance between the ports.
8. The distance between two stations is 300 km. Two trains start simultaneously from these stations and move towards each other. The speed of one of them is 7 km/hr more than that of the other. If the distance between them after two hours of their start is 34 km, find the speed of each train.
9. The difference between the ages of two cousins is 10 years. Fifteen years ago, if the elder one was twice as old as the younger one, find their present ages.
10. Half of a flock of sheep are grazing in the field and three-fourths of the remaining are playing nearby. The rest 9 are drinking water from the river. Find the number of sheep in the flock.