Maths Problems 14 Aug 09

1. In a concert hall, 1/7 of the audience were children. 75% of the adults were women. There were 280 more women than children.

(a) How many women were there in the hall? [2]
(b) During the interval, some men left the hall. As a result, 12% of the remaining audiences were men. How many men left the hall? [3]

2. The base of the container is a square of side 8 cm. Twelve 4-cm cubes are placed in the container. Water is then poured into the container until it is 5/6 full. When all the cubes are removed without any loss of water, the water level drops to 2/3 the height of the container.

(a) Find the volume of the twelve cubes. (1)
(b) Find the height of the container. (4)

3. Amy, Beth and Carrie have some money. If Amy gives $3.50 to Beth, the two girls will have an equal amount of money. If Beth gives $3.50 to Amy, Amy will have thrice as much money as Beth. Carrie’s share is the sum of the other two girls.How much money do they have altogether? (4)

4. Alice left Town X at 8.30 a.m. and travelled towards Town Y at an average speed of 90 km/h. Belinda left Town X 45 minutes later and travelled towards Town Y along the same route at an average speed of 84 km/h.

a) How far apart were they at 10 a.m.? (1m)
b) If Belinda increased her speed by 18 km/h after 10 a.m., how long would it be before she overtakes Alice? (3)

5. A factory was required to produce a certain number of toys in four days.
On the first day, it produced 1/5 of the required number of toys.
On the second day, it produced another 20 toys.
On the third day, it produced as many toys as those produced on the first two days.
On the fourth day, it completed the remaining 8 toys.How many toys did the factory produce in the four days? (4)

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