A man was engaged on a job for 30 days on the condition that he would get a wage of Rs. 10 for the day he works, but he have to pay a fine of Rs. 2 for each day of his absence. If he gets Rs. 216 at the end, he was absent for work for ... days

Let's break down the problem:

1. **Total number of days**: 30
2. **Wage per working day**: Rs. 10
3. **Fine per absent day**: Rs. 2
4. **Total amount received**: Rs. 216

Let \( x \) represent the number of days the man worked. Then the number of days he was absent is \( 30 - x \).

### Formulating the equation:
- The total earnings from the days he worked: \( 10x \)
- The total fine for the days he was absent: \( 2(30 - x) \)

According to the problem, the total amount he received is Rs. 216:
\[
10x - 2(30 - x) = 216
\]

### Solving the equation:
\[
10x - 60 + 2x = 216
\]
\[
12x - 60 = 216
\]
\[
12x = 276
\]
\[
x = \frac{276}{12} = 23
\]

So, the man worked for 23 days.

### Days absent:
The number of days he was absent is:
\[
30 - 23 = 7
\]

Thus, the man was absent for **7 days**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the total amount change if the fine were Rs. 5 per absent day?
2. If the man was absent for 10 days, how much would he have received?
3. How much more would he have earned if he worked all 30 days?
4. What would his total earnings be if the fine was doubled?
5. If the daily wage was Rs. 15 instead of Rs. 10, how many days would he need to work to earn Rs. 250?

**Tip:** When working with word problems, carefully translate the situation into mathematical expressions before solving.

A man was engaged on a job for 30 days on the condition that he would get a wage of Rs. 10 for the day he works, but he has to pay a fine of Rs. 2 for each day of his absence. If he gets Rs. 216 at the end, he was absent for how many days?

Learn how to solve a linear equation problem where a man's earnings depend on his workdays and fines for absences. This problem involves simple arithmetic and linear equations, suitable for students in Grades 6-8. Detailed step-by-step explanation provided.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation