Level 3
A container holds some water up to a height of 71 cm. When 6 identical plastic balls are put into the container, the water level rises by 18 cm. One plastic ball is then removed from the tank, replaced by one metallic ball. The water level increases to 136 cm.

1. Find the ratio of the volume of 1 plastic ball to 1 metallic ball.
2. If the base area of the container is 150 cm², find the difference in the volume between the metallic ball and the plastic ball. Give the answer in cm³.

Level 3
Three cartons, A, B and C, contained 382 marbles. Hazel added some marbles into Carton A and the number of marbles in Carton A tripled. He took out half of the number of marbles from Carton B and added another 98 marbles into Carton C. As a result, the ratio of the number of marbles in Carton A, Carton B and Carton C became 6 : 2 : 9. What was the ratio of the number of marbles in Carton B to the total number of marbles in Carton A and Carton C at first? Give the answer in its lowest term.

Level 3
The prices of two fruits sold at a supermarket is shown.

Grapes: 2 kg for $12
Bananas: 3 kg for $10

1. Mr Lin bought an equal mass of grapes and bananas and spent $64 more on grapes than on bananas. What was the total mass of fruits that Mr Lin bought?
2. Mrs Shay spent an equal amount of money on grapes and bananas. In terms of their masses, what was the ratio of grapes to the ratio of bananas Mrs Shay bought?

Level 3
England and Thailand took part in Youth Games. From England, the ratio of the number of male supporters to the number of female supporters was 1 : 3. From Thailand, the ratio of the number of male supporters to the number of female supporters was 3 : 5. The total number of supporters from England was ²₅ the total number of supporters from Thailand.

1. What was the ratio of the number of male supporters from England to the total number of male supporters from both countries? Express the answer in the simplest form.
2. After 1956 male supporters from both countries left, the percentage of all the female supporters became 74%. How many more female supporters from Thailand than England were there at first?

Level 3
At a conference made up of speakers and participants, there were 10% more men than women. The ratio of the male speakers to female speakers was 8 : 5. There was an equal number of male and female participants.

1. Find the ratio of male speakers to male participants at the conference at first.
2. Halfway, 89 male participants left the conference and another 73 female participants joined the conference. In the end, there were ³₄ as many male participants as female participants remaining behind. How many speakers were there at the conference?

Level 3
Kim, John and Zane started walking at the same time from the same starting point round a circular track. Zane walked in the clockwise direction. Kim and John walked in an anti-clockwise direction. Zane took 6 min to complete each round. He met Kim after every 2 minutes. He met John after every 5 minutes. The three friends keep to their respective speeds throughout their walk.

1. How many rounds did Zane complete in 1 h?
2. When Zane and Kim met again at the starting point after 1 h, John had completed 1.6 km. Find the circumference of the circular track in metres.