Maths Problem Sums 2 July 09

1. There were some commuters in a bus. The ratio of the number of adults to children was 5 : 3. The ratio of the number of boys to the number of girls was 4 : 3. If there were 3 boys more than the number of girls and 5 more men than women, how many men were there in the bus (not including the driver)? (4m)

2. A rectangular fish tank has a layer of coloured marbles covering the bottom of the tank. The volume of the layer of marbles is 6 000 cm3. Water is filled from a tap at a rate of 4 litres per minute until the fish tank becomes 3/4 filled. The capacity of the fish tank is 70 cm by 60 cm by 40 cm. (4m)

(i) Find the volume of the water in the tank.
(ii) How long does it take to fill 3/4 of the fish tank with water?

3. A school bus can carry a total of 30 adults or 45 children. If there were 84 adults and 50 children already seated in 5 school buses, how many more children can be seated in these 5 school buses? (4m)

4. Mrs Tan bought 20 books and pens for $118. One week later, she sold 4 pens. Then she had the same number of pens and books left. Each book cost $1.00 more than each pen. How much did he pay for the books? (5m)

5. Jamie and Stella shared $640 between themselves. When their father gave them another $100 each, Stella had 32% less money than Jamie.
(a) how much money had Stella in the end? (3m)
(b) What was the ratio of Stella’s money to Jamie’s money at first? (2m)

6. There were 150 band members at first. When the number of boys increased by 20% and the number of girls decreased by 10%, the number of children in the band became 165. How many boys were there in the band at first? (5m)

7. The mass of a sack is 48 kg when it is 15/16 filled with rice. Its mass is 39 kg when it is 3/4 filled with rice. What is the mass of the sack when it is half-filled with rice? (3m)