If 12 engines consume 30 metric tonnes of coal when each is running 18h per day, how much coal will be required for 16 engines, each running 24 h per day, it being given that 6 engines of former type consume as much as 8 engines of latter type?
Correct Answer: Description for Correct answer:
Let the required quantity of Coal consumed be x.
More engines, More coal consumption (Direct proportion)
More hours, More coal consumption (Direct proportion)
Less rate of consumption, Less coal consumption (Direct proportion)
Engines 12 : 16 )
) :: 30 : x
Working hours 18 : 24 )
Rate of consumption \( \frac{1}{6} \) : \( \frac{1}{8} \) )
Therefore, => \( \Large m = \frac{1}{4} \times 20 \)
\( \Large 12 \times 18 \times \frac{1}{6} \times x = 16 \times 24 \times \frac{1}{8} \times 30 \)
=> 36x = 1440
Therefore, x = \( \frac{1440}{36} \) = 40
Hence, quantity of coal consumed will be 40 tonnes.
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