| If 12 engines consume 30 metric tonne of coal when each running 18 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? |
A) 10 tonne
B) 5 tonne
C) 25 tonne
D) 40 tonne
Correct Answer: D
Solution :
| 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] |
| \[\left. \begin{align} & \text{Engines}\,\,12:16 \\ & \text{Working}\,\,\text{hours}\,\,18:24 \\ & \text{Rate}\,\,\text{of} \\ & \text{consumption}\,\,\frac{1}{6}:\frac{1}{8} \\ \end{align} \right\}::30:x\] |
| \[\therefore \] \[12\times 18\times \frac{1}{6}\times x=16\times 24\times \frac{1}{8}\times 30\] |
| \[\Rightarrow \] \[36x=1440\] |
| \[\therefore \] \[x=\frac{1440}{36}=40\] |
| Hence, quantity of coal consumed will be 40 tone. |
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