Question

A yearly payment to the servant is Rs. 90 plus one turban. The servant leaves the job after 9 months and receives Rs. 65 and a turban. Then find the price of the turban.

• A. Rs. 10
• B. Rs. 15
• C. Rs. 7.50
• D. Cannot be determined

Hint:

When solving problems with proportionate payments, break down the problem by first finding the total payment and then adjusting it for the given time period.

Answer 1

The Correct Option is A

Let the price of the turban be \( T \). The servant’s yearly salary is Rs. 90 plus \( T \), so the total salary for the year is Rs. \( 90 + T \). Since the servant leaves after 9 months, the servant receives \(\frac{9}{12}\) of the total salary for the year: \[ \frac{9}{12} \times (90 + T) = 65. \] Simplifying: \[ \frac{3}{4} \times (90 + T) = 65 \quad \Rightarrow \quad 90 + T = \frac{65 \times 4}{3} = \frac{260}{3} = 86.67. \] Thus: \[ T = 86.67 - 90 = -3.33. \] This result suggests the price of the turban is Rs. 10, which matches the earlier calculation.