Question

6 men working 9 hours a day can do a piece of work in 4 weeks. How many men are required working 8 hours a day for 3 weeks to complete the same work?

• A. 9 men
• B. 8 men
• C. 5 men
• D. 12 men

Answer 1

The correct option is A 9 men

Here, the number of men is inversely proportional to the number of hours and inversely proportional to the number of days.

Number of men	Number of hours	Number of days
6	9	$4\times 7=28$
$x$	8	$3\times 7=21$
6:$x$	9:8	28:21 = 4:3

$\text{Number of men}\propto \frac{1}{\text{Number of hours}}$
$\Rightarrow 6:x=8:9$ ...(i)

$\text{Number of men}\propto \frac{1}{\text{Number of days}}$
$\Rightarrow 6:x=3:4$ ...(ii)

From (i) and (ii)
6 : $x$
$=\text{compound ratio of}8:9\text{and}3:4$
$\Rightarrow 6:x=(8:9)\times (3:4)$
$\Rightarrow 6:x=(8\times 3):(9\times 4)$
$\Rightarrow 6:x=(24:36)=(2:3)$

$\because$ Product of means = Product of extremes
$\Rightarrow x\times 2=6\times 3$
$\Rightarrow x=9$

Hence, 9 men are required to finish that work in 3 weeks working 8 hours a day.