If 5 persons can weave 160 mats in 8 days, how many mats will 8 persons weave in 6 days?
[amp_mcq option1=”200″ option2=”192″ option3=”190″ option4=”180″ correct=”option2″]
This question was previously asked in
UPSC CAPF – 2013
Let W be the work done (number of mats woven), P be the number of persons, and D be the number of days. We can assume a constant rate of work per person per day.
The total work done is proportional to the number of persons, the number of days, and the individual work rate (R).
$W \propto P \times D \times R$
Assuming the work rate R per person per day is constant for both scenarios, we can write:
$W = k \times P \times D \times R$
Or, more simply, the quantity $W / (P \times D)$ is constant.
$\frac{W_1}{P_1 \times D_1} = \frac{W_2}{P_2 \times D_2}$
In the first case:
$P_1 = 5$ persons
$D_1 = 8$ days
$W_1 = 160$ mats
In the second case:
$P_2 = 8$ persons
$D_2 = 6$ days
$W_2 = ?$ mats
Using the formula:
$\frac{160}{5 \times 8} = \frac{W_2}{8 \times 6}$
$\frac{160}{40} = \frac{W_2}{48}$
$4 = \frac{W_2}{48}$
$W_2 = 4 \times 48$
$W_2 = 192$
So, 8 persons will weave 192 mats in 6 days.