SOLUTION: The weight of a truck without load is 2000 kg. Today the load represents initially 80% of the total weight. At the first stop, they discharge a quarter of the load. What percentage

Question 301972: The weight of a truck without load is 2000 kg. Today the load represents initially 80% of the total weight. At the first stop, they discharge a quarter of the load. What percentage of the total weight does then the load represent?
A) 20% B) 25% C) 55% D) 60% E) 75%

Found 2 solutions by london maths tutor, MathTherapy:
Answer by london maths tutor(243) (Show Source): You can put this solution on YOUR website!
The truck is 2000 kg
Load is 80% of the total weight
Total weight = truck + load
This means: 100% = 20%(weight of the truck) + 80%(weight of the load)
20% --- 2000 kg
1% --- (2000�20)kg = 100kg
80% ---- 80 x 100 = 8000kg
After first stop, 1/4 of the load is discharge.
This means, 3/4 of the load is left on the truck.
3/4 of 8000 kg
= 6000 kg
The new total weight = 6000 + 2000 = 8000 kg
Percentage of the new load = (6000/8000) x 100% = 75%
Answer: (E)
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
The weight of a truck without load is 2000 kg. Today the load represents initially 80% of the total weight. At the first stop, they discharge a quarter of the load. What percentage of the total weight does then the load represent?
Let the weight of the truck be W, and the weight of the load L

Then W + 0L = 2,000, or W = 2,000

Since the load today initially represents 80% of the total weight, then we can say that: L = .8(W + L), but with W = 2,000, we get: L = .8(2,000 + L)

L = 1,600 + .8L
L - .8L = 1,600
.2L = 1,600
L = 8,000

Since of the load was discharged, then , or 2,000 kg was discharged.

Now, with 2,000 kg being discharged, and the original weight being 10,000 kg (weight of truck = 2,000 kg, and initial load = 8,000), then the discharged load (2,000 kg) represents or of the initial total weight (10,000 kg), and which is CHOICE A.

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