Question

An employer engaged a servant with free boarding and lodging for one year with the condition that the servant will be given Rs. 15000 and a cycle at the end of the year. The servant agreed but served the employer only for 9 months and thus received Rs. 11000 and a cycle. The price of the cycle is:

• A. Rs.\ 1100
• B. Rs.\ 1000
• C. Rs.\ 1200
• D. Rs.\ 1500
• E. Rs.\ 1300

Answer 1

The Correct Option is B

Concept: This is a
wages and proportion problem:

• Total payment = Cash + Value of cycle
• Payment is proportional to time worked

Step 1: Let price of cycle be \(x\).
Total yearly payment: \[ 15000 + x \]
Step 2: Use proportional relation.
For 9 months: \[ \frac{9}{12}(15000 + x) = 11000 + x \]
Step 3: Solve equation.
\[ \frac{3}{4}(15000 + x) = 11000 + x \] \[ 11250 + \frac{3x}{4} = 11000 + x \] \[ 11250 - 11000 = x - \frac{3x}{4} \] \[ 250 = \frac{x}{4} \Rightarrow x = 1000 \]
Step 4: Option analysis.

• (A) Rs.\ 1100: Incorrect $\times$
• (B) Rs.\ 1000: Correct \checkmark
• (C) Rs.\ 1200: Incorrect $\times$
• (D) Rs.\ 1500: Incorrect $\times$
• (E) Rs.\ 1300: Incorrect $\times$

Conclusion:
Thus, the correct answer is
Option (B).