1) A tank measuring 60 cm in length and 30 cm in width is filled with water to a height of 10 cm. A bucket is 3⁄4 full of water. Find the amount of water needed to fill the bucket if the ratio of the volume of water in the tank to the volume of water in the bucket is 20 : 3. (Give your answer in litres)
Ans :- 0.9 litres.
2) A tank weighed 26 kg when it was filled with liquid X. When half of liquid X was replaced by liquid Y, the weight became 18 kg. If liquid X was 3 times as heavy as liquid Y, find the weight of the tank when empty.
Ans :- 2 kg.
3) A rectangular tank is 2.4 m long, 0.9 m wide and 80 cm high. It is 5⁄8 filled with water. 85% of the water is transferred to another tank 1.7 m long and 90 cm wide, what will be the height of the water in the second tank?
Ans :- 60 cm.
4) The mass of a book and a bag is 7 kg altogether. The mass of the same book and a box is 11 kg. The mass of the bag and the box is 14 kg. Find the mass of the box.
Ans :- The mass of the box is 9 kg
5) A rectangluar container, 64 cm by 23 cm by 25 cm, is 7⁄10 filled with water.
(a) How many litres of water were there in the container?
(b) Some water was removed from the container and the height of the water level became 12.5 cm. How many litres of water were removed?
Ans :- a) There were 25.76 ℓ of water.
b) 7.36 ℓ of water were removed.
6) Container Y contained 8.3 ℓ of water and Container Z contained 46.79 ℓ of water. An equal amount of water was added to both the containers so that Container Z contained 4 times as much water as Container Y. How much water was added to the containers?
Ans :- 9.06 ℓ water was added to the container.
7) The average mass of Boxes A, B, C and D is 380 kg. It is 90 kg heavier than the average mass of boxes D, E and F. The average mass of boxes A, B and C is 540 kg lesser than the average mass of boxes D, E and F. What is the average mass of boxes A, B, C, E and F?
Ans :- The average mass of boxes A,B,C,E and F is 266kg
8) A tank measuring 50 cm by 20 cm by 60 cm is filled with water to its brim. All the water in the tank is then transferred into cups with a capacity of 200 cm³ each. How many cups are required to hold the water?
Ans :- 300 cups are required to hold the water.
9) Warwick had 423 cubes of edge 5 cm each. He used all of them to build a cuboid with a base as shown below.
(a) Find the height of the cuboid.
(b) If Warwick were to use the 423 cubes to build another cube with an edge of 30 cm instead, how many cubes would he have left?
Ans :- a) Height of the cuboid is 235 cm
b) 207 cubes.
10) Jug X and Jug Y are filled to the brim with water. If all the water in Jug X is poured into Container Z, another 28ℓ of water is needed to completely fill it. If all the water in Jug Y is poured into Container Z, another 35ℓ of water is needed to completely fill it. If the water in Jug X and Y are poured into Container Z together, it will completely fill Container Z.
How much water does Jug X contain when it is 3⁄7 filled with water?
Ans :- Jug X contains 15 ℓ water.