Coal truck
What percentage of the truck's final mass is coal?
Age
14 to 16
Challenge level
Problem
The mass of an empty coal truck before it is loaded is 2000 kg.
At the start of a day it is loaded with coal, and the coal makes up 80% of the total mass.
At the first delivery, the driver unloads a quarter of the coal.
Can you express the mass of coal left on the truck, as a percentage of the total mass, after the driver made the first delivery?
This problem is adapted from the World Mathematics Championships
Student Solutions
Answer: 75%
Using ratio
At the beginning of the day, the mass of the truck is 80% coal and 20% truck.
Ratio of truck : coal is 1 : 4
Image
Image
Image
Image
Image
At the first delivery, the truck loses $\frac14$ of the coal:
Image
Image
Image
Image
Image
So the ratio of truck : coal is 1 : 3. That is equivalent to 25% : 75%.
So 75% of the truck's mass is coal after the first delivery.
Finding the total mass of the truck and the load
Image
$6000$ kg coal
total mass $8000$ kg.
$\dfrac{6000}{8000}=\dfrac34=75\%$ of the total mass is coal.