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Q1. (a) A cruise line contracts to purchase two identical ships at a cost of £364 M each.

During construction of the first ship the costs of labour and materials are in the ratio of 3:4 and the ship builders make a profit of 4%.

Determine EACH of the following:

(i) the cost of the materials for the first ship; (5)

(ii) the percentage profit made on the second ship if the labour costs have increased by 2% and the material costs have decreased by 5%. (5)

(b) The ratio of the volumes of two solid cubes is 729:64.

Determine the side length of the larger cube if the surface area of the smaller cube is 384 cm². (6)