Question

40 workers working for 8 hours per day digs a hole of 1088$m^3$. If 45 workers work for 6 hours a day, then what volume of the hole they can dig?

• A. $928m^3$
• B. $818m^3$
• C. $908m^3$
• D. $918m^3$

Answer 1

The correct option is D $918m^3$

Here, the number of workers is directly proportional to the number of hours per day and volume of hole.

Number of workers	Number of hours a day	Volume of hole
40	8	$1088m^3$
45	6	$x$
40:45 = 8:9	8:6 = 4:3	1088: $x$

Number of workers $\propto$ Volume of the hole
$\Rightarrow 8:9=1088:x...\left(i\right)$
Number of hours a day $\propto$ Volume of the hole
$\Rightarrow 4:3=1088:x...\left(ii\right)$

From (i) and (ii), we get,
1088 : $x$
$=\text{compound ratio of}8:9\text{and}4:3$

$\Rightarrow 1088:x=(8:9)\times (4:3)$
$\Rightarrow 1088:x=(8\times 4):(9\times 3)$
$\Rightarrow 1088:x=(32:27)$

$\because$ Product of means = Product of extremes
$\Rightarrow x\times 32=1088\times 27$
$\Rightarrow x=918m^3$