Question

A man engaged a servant on the condition that he would pay him Rs 90 and a turban after a service of one year. He only served for nine months and received the turban and Rs 65. The price of the turban is?
A. Rs 25
B. Rs 18.75
C. Rs 10
D. Rs 2.50

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 turban $ = T$
One year payment of the servant $ = 90 + T$ (he will receive payment after one year means 12 months)
12 Month’s payment $ = 90 + T$
1 Month payment $ = \dfrac{{90 + T}}{{12}}$
Therefore 9 month payment $ = \dfrac{{(90 + T)}}{{12}} \times 9$ Equation (i)
 By unitary method we have found out one month payment and then nine month payment.
Servant works for $9$ months and receive payment $ = 65 + T$ Equation (ii)
As both the equations are equal in meaning so we will equate them to find out the price of the turban.
$ \Rightarrow \dfrac{{(90 + T) \times 9}}{{12}} = 65 + T$ (Cancelling out numerator and denominator)
 $ \Rightarrow \dfrac{{(90 + T) \times 3}}{4} = 65 + T$ (Cross multiplying)
$ \Rightarrow 270 + 3T = 260 + 4T$
$ \Rightarrow 4T - 3T = 270 + 260$
$ \Rightarrow T = 10$
Hence the final answer for the price of the turban is Rs 10

So, the correct answer is “Option C”.

Note: Students may likely make mistakes while not converting the units in question. It is mentioned one year as well as 12 months so while solving units must be the same so we cannot solve with different units. Questions can be solved in either unit depending upon the given data.