3.
If 9 engines consume 24 metric tonnes of coal, when each is working 8 hours
day,
bow much coal will be required for 8 engines, each running 13hours a day, it
being given that 3 engines of former type consume as much as 4 engines of
latter type?
Answer:
Let 3 engines of former type consume 1 unit in
1 hour.
Then,
4 engines of latter type consume 1 unit in 1 hour.
Therefore
1 engine of former type consumes(1/3) unit in 1 hour.
1
engine of latter type consumes(1/4) unit in 1 hour.
Let
the required consumption of coal be x units.
Less
engines, Less coal consumed (direct proportion)
More
working hours, More coal consumed (direct proportion)
Less
rate of consumption, Less coal consumed(direct prportion)
Number
of engines 9: 8
Working
hours 8 : 13 } :: 24 : x
Rate
of consumption (1/3):(1/4)
[
9 x 8 x (1/3) x x) = (8 x 13 x (1/4) x 24 ) 24x = 624 x = 26.
Hence,
the required consumption of coal = 26 metric tonnes.
