Question

# A labourer earns $Rs.{\rm{ 1980}}$ in $12$ days. In how many days will he earn $Rs.{\rm{ 2640}}$.

Hint:Here we are going to use the unitary method to solve this problem. That is we have to find money earned by the man in one day and then with the help of the amount we can find how many days the man requires to earn the given amount.

Now we have a labourer earn $Rs.{\rm{ 1980}}$ in $12$ days.
By the unitary method first we have to find quantity of single unit value
Therefore, now we are going to find a labourer who earns money for one day. Dividing earned money $Rs.{\rm{ 1980}}$ by the number of days to earn that money. It is $12$ days.
Hence,
$\Rightarrow {\rm{ }}\dfrac{{1980}}{{12}}$
Cancelling the numerator and denominator by $4$ we get,
$\Rightarrow {\rm{ }}\dfrac{{1980}}{{12}} = \dfrac{{495}}{3}$
Cancelling the numerator and denominator by $3$ we get,
$\Rightarrow {\rm{ }}\dfrac{{495}}{3} = \dfrac{{165}}{1} = Rs.{\rm{ }}165$
Therefore a labourer earns $Rs.{\rm{ }}165$ in one day.
Again using the unitary method we have to multiply the single unit value into our required value.
Now we have to find how many days a labourer takes to earn $Rs.{\rm{ 2640}}$.
Hence we have to divide$Rs.{\rm{ 2640}}$by$Rs.{\rm{ }}165$that is the amount earned by the person in a day.
$\Rightarrow {\rm{ }}\dfrac{{2640}}{{{\rm{165}}}}$
$\Rightarrow {\rm{ 16}}$
Now we find ${\rm{16}}$ days takes a labourer to earn $Rs.{\rm{ 2640}}$.

Additional Information:Unitary method: The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value. In essence, this method is used to find the value of a unit from the value of a multiple, and hence the value of a multiple.

Note:Here we have to divide the amount earned by the labourer in 12 days by 12 to get the amount earned in a single day. It is asked that we have to find the number of days to earn the given amount. That is we have divided the given amount by the amount earned by man in a day. Suppose we are given to find the amount and days are given we should multiply the days with the amount earned in a day.