LINEAR EQUATIONS

1. Solve the following equations and check your result.
a) 2(5x-3) -3 (2x -1) = 9 (b) x - (7 – 8x) = 2 c) (x +1)2 = x + 2 /5 d) 9x - 1/2(3 + 4x) = 3

2. When 4 is subtracted from three times a number and the result is divided by 3 more than the number, we get 2/5. Find the number.
3. A number is as much greater than 84 as it is less than 108. Find the number.
4. A number consists of two digits whose sum is 9. If 9 is added to the number, its digits are reversed. Find the number.
5 The digit is unit’s place of a two digit number is three times that in the ten’s place. If the digits are reversed, the new number is 36 greater than the original number. Find the number.
6. A steamer goes down stream form one port to another in 5 hours while it covers the same distance upstream in 6 hours. If the speed of the stream is 3 kmph, find the speed of the steamer in still water.
7. The distance between two station A and B is 290 km. Two motorcyclists start simultaneously form A and B towards each other and the distance between them after 3 hours is 20km. IF the speed of one motorcyclist is less than the other by 10 kmph, find the speed of each motorcyclist.
8. The denominator of a fraction exceeds numerator by 3. IF numerator is doubled and the denominator is increased by 14, the fraction becomes rd of the original fraction. Find the fraction.
9. The length of a rectangle exceeds its breadth by 4 cm. IF length and breadth are each increased by 3 cm, the area of the new rectangle will be 57 cm2 more than that of the original rectangle. Find the length and breadth of the given rectangle.
10. Five years ago, a man was seven times as old as his son. After 5 years, he will be 3 times as old as his son. Find their present ages.

AREA, SURFACE AREA, VOLUME

1 ) The volume of a circular pipe of length 1metre is 3850 cu .cm. Find its diameter.

2 ) A cylinder is open at one end. The external diameter is 10 cm and thickness 2 cm .If height is 8 cm ,find
a) Capacity of the cylinder
b) Volume of metal used

3) Find the number of coins 1.5 cm in diameter and 0.2 cm thick to be melted to form a right circular cylinder of height 16 cm and diameter 6 cm.

4) A rectangular paper of width 30 cm and length 77 cm is rolled along its width ,to form a cylinder.What is the volume of the cylinder formed.

5) A conical tent is 9 m high and radius of its base is 12 m.
a) What is the cost of canvas required to make ir ,if one square metre of canvas costs Rs10
b) How many persons can be accommodated in the tent,if each person requires 2 square metre of ground and 15 m3 of space to breathe in?

6) The diameter of a road-roller is 84Cm and its length is 120cm. It takes 500 complete revolutions to level a playground. Find area of the playground in sq .m.

7) A solid right circular cylinder of diameter 16cm and height 2cm is melted and cast into a right circular cone of height 3 times that of the cylinder. Find the curved surface area of the cone.

8) The dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of Rs.498.96. If the rate of white-wash is Rs.2 per sq. metre, find
a) Inside surface area of the dome.
b) The volume of the air inside the dome.

9) A well is dug 20m deep and has a diameter of 7m. The earth which is spread on a rectangular plot, 22m long and 14m broad. What is the height of the platform that is formed?

10) A conical cup 9cm high, has a circular base of diameter 14cm. The cup is full of water which is now poured into a cylindrical vessel of diameter 10cm. What will be the height of the water in the vessel?

11) Curved surface area of a cone is 308 sq. cm and its slant height is 14cm. Find the total surface area of the cone.

12) The radii of two circles are 5cm and 12cm. The area of a third circle is equal to the sum of the areas of the two circles. Find the radius of the third circle.

13) From a rectangular sheet of sides 30cm and 40cm, a circular sheet as big as possible is cut off. Find the area of the remaining part.

14) The volume of the conical tent is 1232 cu.m and the area of its base is 154 sq.m. Find the length of canvas required to build the tent if canvas is 2m in width.

15) A cylindrical road-roller made of iron is 1m wide. Its inner diameter is 54cm and thickness of the iron sheet rolled into the road-roller is 9cm. Find the weight of roller if 1c.c. of iron weighs 8g.

16) Find the number of coins, 1.5cm in diameter and 0.2 cm thick, to be melted to form a right circular cylinder of height 10cm and diameter 4.5cm.

17) A hemispherical bowl is made of steel 0.25cm thick. Inside radius of the bowl is 5cm. Find the volume of steel used in making the bowl.

18) A wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base of the cone is 6cm and its height is 4cm. Find the cost of painting the doll at the rate of Rs.5 per thousand sq.cm.

19) The altitude of a triangle is five-thirds the length of its base. If the altitude was increased by 4cm and the base decreased by 2cm, the area of the triangle would remain the same. Find the base and altitude of the triangle.

20) The area of a trapezium is 91 sq.cm and height is 7cm. If one of the parallel sides is longer than the other by 8cm, find the length of the parallel sides.

21) The parallel sides of a trapezium are 25cm and 13cm. Its non-parallel sides are equal, each being 10cm. Find the area of the trapezium.

22) The area of an equilateral triangle is 16√3 sq.cm. Find the length of each side of the triangle.