Question

One year payment of the servant is one shirt and Rs$200$.The servant leaves after 9 months and receives Rs $120$ and a shirt. What is the price of the shirt?
a. $Rs80$
b. $Rs100$
c. $Rs120$
d. Can’t be determined

Answer 1

Hint: Here this question can be solved by unitary method. Unitary method is a technique in which we first find out the value of a single unit and then multiplying that unit to find necessary values.
For example: - $20$ Apples $ = Rs100$
                      $1$ Apple $ = \dfrac{{Rs100}}{{20}} = Rs5$
                      $5$ Apples $ = 5 \times Rs5 = Rs25$
So, from the above example it is clear how to apply the unitary method in questions.

Complete step-by-step answer: Let the price of the shirt $ = s$
One year payment of the servant $ = 200 + s$ (he will receive payment after one year means $12$ months)
$12$Month’s payment $ = 200 + s$
$1$ Month payment $ = \dfrac{{200 + s}}{{12}}$
$\therefore $$9$ Month payment $ = \dfrac{{(200 + s)}}{{12}} \times 9.........................(i)$
 By unitary method we have found out one month payment and then nine month payment.
Servant works for $9$ months and receive payment $ = 120 + s......................(ii)$
As both the equations are equal in meaning so we will equate them to find out the price of a shirt.
$ \Rightarrow \dfrac{{(200 + s) \times 9}}{{12}} = 120 + s$ (Cancelling out numerator and denominator)
$ \Rightarrow \dfrac{{(200 + s) \times 3}}{4} = 120 + s$ (Cross multiplying)
$ \Rightarrow 600 + 3s = 480 + 4s$
$ \Rightarrow s = 120$
Hence the final answer for the price of a shirt is option C i.e. Rs$120$

Note: Unitary method has two types of variations: -
1. Direct variation: - In this type of variation an increase or decrease in one quantity will cause an increase or decrease of another quantity. For example – Increase in the number of goods causes an increase in price of goods so they are directly related to each other.
2. Indirect variation: - In this type of variation an increase or decrease in one quantity will cause a decrease or increase of another quantity. For example - Increase in speed can cause decrease in the total distance which has to be covered.