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.

Given,

Number of remaining boxes in the three trucks are in the ratio 4 : 6 : 5.

So, let remaining boxes be

In first truck = 4x, second truck = 6x and third truck = 5x

Total boxes including rotten boxes in each truck are

In first truck = 4x + 7, second truck = 6x + 12 and third truck = 5x + 8

Total boxes = 1077

⇒ 4x + 7 + 6x + 12 + 5x + 8 = 1077

⇒ 15x + 27 = 1077

⇒ 15x = 1077 - 27

⇒ 15x = 1050

⇒ x = $\dfrac{1050}{15}$ = 70.

So, no. of boxes :

In first truck = 4x + 7 = 4(70) + 7 = 280 + 7 = 287,

second truck = 6x + 12 = 6(70) + 12 = 420 + 12 = 432,

third truck = 5x + 8 = 5(70) + 8 = 358.

Hence, no. of boxes originally in each truck were 287, 432 and 358.