Question

If 20 typists typing 5 hours a day can type a novel in 15 days, then, how many days will 15 typists working 6 hours a day can take to do the same job?

• A. 19 days
• B. 24 days
• C. 18 days
• D. 20 days

Answer 1

The correct option is B 24 days

Here, the number of typists is inversly proportional to the number of hours and to the number of days required to type a novel.

Number of typists	Number of hours	Number of days
20	6	10
$x$	5	15
20:$x$	6:5	10:15 = 2:3

When the number of days is fixed, then
$\text{Number of typists}\propto \frac{1}{Numberofhours}$
$\Rightarrow 20:x=5:6...\left(i\right)$

When the number of hours per day is fixed, then
$\text{Number of typists}\propto \frac{1}{Numberofdays}$
$\Rightarrow 20:x=3:2...\left(ii\right)$
From (i) and (ii), we get,
$20:x=\text{compound ratio of}5:6\text{and}3:2$
$\Rightarrow 20:x=(5:6)\times (3:2)$
$\Rightarrow 20:x=(5\times 3):(6\times 2)$
$\Rightarrow 20:x=(15:12)\text{or}(5:4)$

$\because$ Product of means = Product of extremes
$\Rightarrow x\times 5=20\times 4$
$\Rightarrow x=\frac{20\times 4}{5}=16typists$

So, 16 typists will be needed to complete the work in 15 days working 5 hours a day.