If 9 engines consume 24 metric tons of coal, when each is working 8 hours per day, how much coal should be available for 8 engines, each running 13 hours per day, it is given that 3 engines of the former type consume as much as 4 engines of the latter type.

Question: If 9 engines consume 24 metric tons of coal, when each is working 8 hours per day, how much coal should be available for 8 engines, each running 13 hours per day, it is given that 3 engines of the former type consume as much as 4 engines of later type.

Solution:
We have:
The lesser engines, less coal consumed
More working hours, more coal consumed
Both the cases are directly proportional.
If three engines of former type consume 1 unit, 1 engine will consume 1/3 unit.
If four engines of latter type consume 1 unit, 1 engine will consume ¼ units.
And, less rate of consumption, less coal consumed.
Now, Number of engines = 9: 8
Working hours = 8:13
Therefore, rate of consumption = 1/3 : 1/4

Let the coal consumed by 8 engines is x metric tones
9 × 8 × 1/3 : 8 × 13 × 1/4 = 24 : x
⇒ 9 × 8 × (1/3) × x = 8 × 13 × (1/4) × 24
⇒ 24x = 624
∴ x = 26