Discussion Forum

 If 9 engines consume 24 metric tonnes of coal, when each is working 8 hours a day, how much coal will be required for 8 engines, each running 13 hours a day, it being given that 3 engines of former type consume as much as 4 engines of latter type?

Answer:

Explanation:

Let 3 engines of former type consume 1 unit in 1 hour.

Then, 4 engines of latter type consume 1 unit in 1 hour.

1 engine  of  former  type  consumes $\frac{1}{3}$ unit in 1 hour. 

1 engine of latter type consumes $\frac{1}{4}$ 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 Proportion)

$\left\{\begin{array}{c}No.engines\quad\quad\quad\quad\quad\quad\quad\quad 9:8\\ Working\quad hours\quad\quad\quad\quad\quad\quad 8:13\\Rate\quad of\quad consumption\quad\quad\quad\frac{1}{3}:\frac{1}{4}\end{array}\right\}::24:x$

$\therefore \left(9\times 8\times\frac{1}{3}\times x\right)$ $=\left(8\times 13\times\frac{1}{4}\times 24\right)$

$\Leftrightarrow 3x=78$  $\Leftrightarrow x=26$