A labourer is engaged for 30 days on the condition that he will receive ₹25 for each day he works and will be fined ₹7.50 for each day he is absent. If his total earnings at the end of the period are ₹425, for how many days was he absent from work?

Introduction / Context:
This question blends Time and Work ideas with simple arithmetic about wages and penalties. The labourer is paid a fixed amount per working day and fined a smaller amount per day of absence. Given the total number of days in the contract and his final earnings, we are asked to determine the number of days he was absent. Such problems commonly appear in aptitude tests under the category of wages, work and simple equations.

Given Data / Assumptions:

• Total contract period = 30 days.
• Earning per working day = ₹25.
• Fine per absent day = ₹7.50.
• Total money received by the labourer = ₹425.
• Every day is either a working day or an absent day (no partial days).

Concept / Approach:
Let the number of working days be w and the number of absent days be a. We know that w + a = 30. His total earnings are calculated as (w * wage per day) minus (a * fine per day). Using these two relationships, we form two linear equations in w and a, then solve to find the value of a, which gives the number of days of absence.

Step-by-Step Solution:
Let w = number of days he actually worked. Let a = number of days he was absent. Total days: w + a = 30. ...(1) Earnings on working days = 25w. Fine on absent days = 7.5a. Net amount received = earnings - fines = 25w - 7.5a. Given that 25w - 7.5a = 425. ...(2) From equation (1), w = 30 - a. Substitute into (2): 25(30 - a) - 7.5a = 425. This gives 750 - 25a - 7.5a = 425. Combine like terms: 750 - 32.5a = 425. Rearrange: 32.5a = 750 - 425 = 325. a = 325 / 32.5 = 10. Therefore, the labourer was absent for 10 days.

Verification / Alternative check:
If a = 10 days, then w = 30 - 10 = 20 working days. Earnings without fines would be 20 * 25 = ₹500. Fines for 10 absent days total 10 * 7.5 = ₹75. Net amount = 500 - 75 = ₹425, which perfectly matches the given total earnings. This confirms that 10 days of absence is correct.

Why Other Options Are Wrong:
If he were absent 9 days, he would have worked 21 days. Net earnings would be 21 * 25 - 9 * 7.5 = 525 - 67.5 = ₹457.50, not ₹425. Similarly, for 11 or 14 days of absence, the computed net earnings do not match ₹425. Only 10 days of absence yields the correct final amount.

Common Pitfalls:
One frequent mistake is to add the fine instead of subtracting it, leading to a higher net amount. Another is to mis-handle the decimal 7.5 when solving the equation. To avoid confusion, some students prefer to multiply the entire equation by 2 or 10 to eliminate decimals before solving. Also, forgetting that the total number of days is fixed at 30 can lead to incorrect systems of equations.

Final Answer:
The labourer was absent from work for 10 days.