Q1. (a) An alloy is made by combining metal A with metal B so that the ratio of their volumes is 7:5. The relative density of metal A is 8.4 and that of metal B is 9.6.
Determine the percentage mass of EACH of the metals in the alloy.
(b) A person spends £24750 in starting a business venture. This sum comprises the cost of buying the premises, the cost of repairs to the premises and the cost of equipment to be installed.
The cost of repairs was 10% of the purchase price and the cost of equipment was 12.5% of the combined price of the purchase price and the cost of repairs. Calculate EACH of the following:
(i) The purchase price; (ii) The cost of repairs; (iii) The cost of equipment.
Q6. (a) Two ships approach the same port. Their courses converge at an angle of 23°. At 1900 hours, the two ships are 32 nautical miles apart and one ship is twice as far from the port as the other.
Calculate how far EACH ship is from the port at 1900 hrs.
Q9. A solid metal cylinder of diameter 20 cm and length 36 cm has six holes drilled through it as shown in Fig Q9. All six holes have a diameter of 3 cm and are drilled parallel to the axis of the cylinder.
Calculate EACH of the following:
(a) The total surface area of the original cylinder;
(b) The percentage increase in the total surface area after the six holes have been drilled;
(c) The percentage decrease in volume of the solid.
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