1077 boxes of oranges were loaded in three trucks. While unloading them 7, 12 and 8 boxes were found rotten in the trucks respectively. If the number of remaining boxes in the three trucks are in the ratio 4 : 6 : 5, find the number of boxes loaded originally in each truck.

If a ≠ b and a : b is the duplicate ratio of (a + c) and (b + c), show that a, c and b are in continued proportion.

Show that 2x + 7 is a factor of 2x³ + 7x² - 4x - 14. Hence, solve the equation :

2x³ + 7x² - 4x - 14 = 0.