Question

In one shift of 8 hours, 28 tea-pluckers can pluck 1260kg of green leaves. By how much can the workforce can be reduced if the same amount of green leaves is to be plucked in $14$ hours?

Answer 1

Hint: It is quite evident from the question that if the number of hours gets increased to $14$ then the fewer number of tea-pluckers will be needed to pluck the same amount of rea leaves, i.e., $1260kg$. This explains they are inversely proportional to each other;
$x \propto \dfrac{1}{y}$ ; proportional sign is replaced with a constant. So, $xy = k$
That is, their product must be constant.

Complete step by step answer:
It is quite clear from the question that as the number of hours for which the tea pluckers work will increase, for the same amount of tea leaves, the number of tea pluckers will decrease.
There exists an inverse relationship between them.
So, what we need to understand is that in both cases their product must remain the same. ..(1)
Let the number of tea-pluckers required to complete the same amount of work in $14$ hours be x.
Therefore,
$
\Rightarrow 28 \times 8 = x \times 14 \\
\Rightarrow x = \dfrac{{28 \times 8}}{{14}} \\
\Rightarrow x = 2 \times 8 \\
\Rightarrow x = 16 \\
 $ (using (1))
The number of tea-pluckers required will be $16$.

Initially, to complete the same amount of work, $28$tea-pluckers were required.
So, the work force is reduced by ($28 - 16 = 12$)hours.

Note:
 In these type of questions, try to notice that which of the quantity remains unchanged and then keep it out of the calculation. Then, check out what kind of relationship (direct or inverse) exists between the remaining variables.