Question

A worker earns Rs.18,000 in 15 months.
(a) How much will the worker earn in 7 months?
(b) In how many months will he earn Rs.3,600?

Answer 1

Hint: We solve this problem by first acknowledging that the number of months the worker has worked is proportional to the amount he earns. Then we use the property of proportionality, if x and y are proportional, then \[\dfrac{x}{y}=constant\]. Then we use it to find the relation between the number of months and the amount the worker earned. Then we use this relation and substitute the given values and solve them to find the required values in each subpart.

Complete step-by-step solution
We are given that a worker earns Rs.18,000 in 15 months.
As we see if the worker works for more months then the amount he earns increases, that is if the number of months increases then the earning of the worker increases.
So, we can say that Number of months is proportional to the amount earned by the worker.
Now, let us consider the property of proportionality, if x and y are proportional, then
\[\dfrac{x}{y}=constant\]
So, using this, we get that,
$\Rightarrow \dfrac{Number\ of\ months}{Amount\ earned\ by\ the\ worker}=constant$
(a) How much will the worker earn in 7 months?
From above we have the formula,
$\Rightarrow \dfrac{Number\ of\ months}{Amount\ earned\ by\ the\ worker}=constant$
Now, as we are given that the worker earns Rs.18,000 in 15 months, we can write it as,
$\Rightarrow \dfrac{Number\ of\ months}{Amount\ earned\ by\ the\ worker}=\dfrac{15}{18000}$
As we need to find the amount, he earns in 7 months, let us substitute it in the above equation. Then we get,
\[\begin{align}
  & \Rightarrow \dfrac{7}{Amount\ earned\ by\ the\ worker}=\dfrac{15}{18000} \\
 & \Rightarrow Amount\ earned\ by\ the\ worker=\dfrac{18000}{15}\times 7 \\
 & \Rightarrow Amount\ earned\ by\ the\ worker=1200\times 7 \\
 & \Rightarrow Amount\ earned\ by\ the\ worker=8400 \\
\end{align}\]
Hence the answer is Rs.8,400.
(b) In how many months will he earn Rs.3,600?
From above we have the formula,
$\Rightarrow \dfrac{Number\ of\ months}{Amount\ earned\ by\ the\ worker}=constant$
Now, as we are given that the worker earns Rs.18,000 in 15 months, we can write it as,
$\Rightarrow \dfrac{Number\ of\ months}{Amount\ earned\ by\ the\ worker}=\dfrac{15}{18000}$
As we need to find the number of months he takes to earn Rs.3600, let us substitute it in the above equation. Then we get,
\[\begin{align}
  & \Rightarrow \dfrac{Number\ of\ months}{3600}=\dfrac{15}{18000} \\
 & \Rightarrow Number\ of\ months=\dfrac{15}{18000}\times 3600 \\
 & \Rightarrow Number\ of\ months=\dfrac{54000}{18000} \\
 & \Rightarrow Number\ of\ months=3 \\
\end{align}\]
Hence the answer is 3 months.

Note: The common mistake one makes while solving this question is one might take the property of proportionality wrongly as, $xy=constant$. But it is the case for inversely proportional. Here the number of months the worker had worked is proportional to the amount he earns, so we need to take the formula \[\dfrac{x}{y}=constant\].