An employer engaged a servant with free boarding and lodging for one year with…
2024
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:
Answer: A. Rs 1000 — ConceptWhen payment for a job is proportional to the time actually served, the fraction of the total agreed period worked must equal the fraction of the total…
- A.
Rs 1000
- B.
Rs. 1250
- C.
Rs 800
- D.
Rs 900
Attempted by 1 students.
Show answer & explanation
Correct answer: A
Concept
When payment for a job is proportional to the time actually served, the fraction of the total agreed period worked must equal the fraction of the total agreed payment (cash plus any non-cash item, like a cycle) received. This lets us set up a proportion between the time served and the value received to solve for an unknown in-kind component of the payment.
Application
Let the price of the cycle be Rs. x. The full annual package for 12 months is Rs. (15000 + x).
The servant worked only 9 months, i.e. 9/12 of the year, and received Rs. (11000 + x) — the same cycle plus the reduced cash amount.
Since payment is proportional to time served: (9/12) × (15000 + x) = 11000 + x
Multiplying out: 0.75 × 15000 + 0.75x = 11000 + x, i.e. 11250 + 0.75x = 11000 + x
Rearranging: 11250 − 11000 = x − 0.75x, i.e. 250 = 0.25x
Solving: x = 250 / 0.25 = 1000
Cross-check
Check: for 12 months the total value is Rs. 15000 + Rs. 1000 = Rs. 16000. For 9 months (3/4 of the year) the servant should receive 3/4 × 16000 = Rs. 12000 in total value, i.e. Rs. 12000 − Rs. 1000 (cycle) = Rs. 11000 in cash — exactly matching the given Rs. 11000.
Hence, the price of the cycle is Rs. 1000.
