Question

A labourer earns Rs. 1980 in 12 days.
(i) How much does he earn in 7 days?
(ii) In how many days will he earn Rs. 2640?

Answer 1

Hint: Start with finding out the per day’s earning of the labourer using a unitary method. Then his 7 day’s earning will be 7 times his per day’s earning. And the number of days required by him to earn Rs. 2640 can be calculated by dividing Rs. 2640 by his per day’s earnings.

Complete step-by-step answer:
According to the question, the labourer earns Rs. 1980 in 12 days.
(i) The amount earn by him per day can be calculated using unitary method:
$ \Rightarrow $ Amount earn by the labourer per day $ = \dfrac{{{\text{Rs}}{\text{. 1980}}}}{{12}} = {\text{ Rs}}{\text{. 165}}$
Thus his per day’s earning is Rs. 165.
Therefore the amount earn by him in 7 days is given as:
$ \Rightarrow $ Amount earn by him in 7 days $ = 7 \times $ Per day’s earning
Putting the value of per day’s earning, we’ll get:
$ \Rightarrow $ Amount earn by him in 7 days $ = 7 \times {\text{ Rs}}{\text{. }}165 = {\text{ Rs}}{\text{. }}1155$.
Hence, he earned Rs. 1155 in 7 days.
(ii) As calculated above, his per day’s earning is Rs. 165.
The number of days required for him to earn Rs. 2640 is given as:
$ \Rightarrow $ No. of days required to earn Rs. 2640 $ = \dfrac{{{\text{Rs}}{\text{. 2640}}}}{{{\text{Per day's earning}}}}$
Again putting the value of per day’s earning, we’ll get:
$ \Rightarrow $ No. of days required to earn Rs. 2640 $ = \dfrac{{{\text{Rs}}{\text{. 2640}}}}{{165}} = 16$

Hence, he will earn Rs. 2640 in 16 days.

Note: In unitary method, we solve the problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value. This method is widely used in ‘Time & Work’ problems.
Time is directly proportional to work, with increase in time the amount of work done will also increase.