Question

If ₹42,000 is spent on wages of 12 men working for 30 days, then what amount would have been spent if there were 18 men working for 24 days?

• A. ₹50,400
• B. ₹50,000
• C. ₹55,000
• D. ₹48,400

Answer 1

The correct option is A ₹50,400

Here, the wages are directly proportional to the number of men and also to the number of days.

Number of men	Wages	Number of days
12	₹42,000	30
18	$x$	24
12:18 = 2:3	42000:$x$	30:24 = 5:4

Wages $\propto$ Number of men
$\Rightarrow 42000:x=2:3...\left(i\right)$

Wages $\propto$ Number of days
$\Rightarrow 42000:x=5:4...\left(ii\right)$

From (i) and (ii), we get,
$42000:x=\text{compound ratio of}2:3\text{and}5:4$
$\Rightarrow 42000:x=(2:3)\times (5:4)$
$\Rightarrow 42000:x=(2\times 5):(3\times 4)$
$\Rightarrow 42000:x=(10:12)or(5:6)$

$\because$ Product of means = Product of extremes
$\Rightarrow x\times 5=42000\times 6$
$\Rightarrow x=50400$

So, ₹50,400 would have been spent if there were 18 men working for 24 days.