(a) A dealer sold a car to a man and made a profit of 15%. The man then sold it to a woman for N120,175.00 at a loss of 5%. How much did the dealer buy the car? (b) The diameter of the wheel of a car is 36cm. How many revolutions, correct to three significant figures, will it make to cover a distance of 1.05 km? [Take \(\pi = \frac{22}{7}\)].
Explanation
(a) Let the cost of the car to the dealer be x. Sales of car to a man with 15% profit : (115% of x = 1.15 x\) Sale of the car to the woman by the man at 5% loss : (95% of 1.15x = N120,175.00) \(0.95 \times 1.15x = N120,175.00\) \(1.0925x = N120,175.00\) \(x = \frac{120,175.00}{1.0925}\) \(x = N110,000\) The original cost of the car to the dealer = N110,000.00. (b) Circumference of a circle = \(2\pi r\) Distance covered by the wheel = 1.05 km Radius of the wheel = 18cm Circumference of the wheel = \(2 \times \frac{22}{7} \times 18\) = \(113.14 cm\) Note : 1.05 km = 105,000 cm Number of revolution = \(\frac{105,000}{113.14}\) = \(928.05 revs\) \(\approxeq 928 revs\)