In a particular week, the average earning per day of a plumber from Monday to Wednesday remained ₹580 and from Thursday to Saturday it was ₹612. If the average earning for the whole week was ₹675, then how much did he earn on Sunday?
₹1149
Calculating Plumber's Sunday Earning
This problem asks us to find the plumber's earning on Sunday, given the average earnings for different periods of the week and the overall average for the entire week. We need to use the concept of average and total earnings to solve this.
The average is calculated as:
$$\text{Average Earning} = \frac{\text{Total Earning}}{\text{Number of Days}}$$
From this, we can find the total earning for a period:
$$\text{Total Earning} = \text{Average Earning} \times \text{Number of Days}$$
Step-by-Step Calculation
1. Calculate Total Earning from Monday to Wednesday
The average earning from Monday to Wednesday was ₹580 for 3 days.
Number of days = 3 (Monday, Tuesday, Wednesday)
Average earning = ₹580
Total earning (Mon-Wed) = Average Earning $\times$ Number of Days
Total earning (Mon-Wed) = ₹580 $\times$ 3
Total earning (Mon-Wed) = ₹1740
2. Calculate Total Earning from Thursday to Saturday
The average earning from Thursday to Saturday was ₹612 for 3 days.
Number of days = 3 (Thursday, Friday, Saturday)
Average earning = ₹612
Total earning (Thu-Sat) = Average Earning $\times$ Number of Days
Total earning (Thu-Sat) = ₹612 $\times$ 3
Total earning (Thu-Sat) = ₹1836
3. Calculate Total Earning from Monday to Saturday
The total earning from Monday to Saturday is the sum of the earnings from Monday to Wednesday and from Thursday to Saturday.
Total earning (Mon-Sat) = Total earning (Mon-Wed) + Total earning (Thu-Sat)
Total earning (Mon-Sat) = ₹1740 + ₹1836
Total earning (Mon-Sat) = ₹3576
4. Calculate Total Earning for the Whole Week (Monday to Sunday)
The average earning for the whole week (7 days) was ₹675.
Number of days = 7 (Monday to Sunday)
Average earning = ₹675
Total earning (Mon-Sun) = Average Earning $\times$ Number of Days
Total earning (Mon-Sun) = ₹675 $\times$ 7
Total earning (Mon-Sun) = ₹4725
5. Calculate Earning on Sunday
The total earning for the whole week is the sum of the total earning from Monday to Saturday and the earning on Sunday.
Total earning (Mon-Sun) = Total earning (Mon-Sat) + Earning on Sunday
We can rearrange this formula to find the earning on Sunday:
Earning on Sunday = Total earning (Mon-Sun) - Total earning (Mon-Sat)
Earning on Sunday = ₹4725 - ₹3576
Earning on Sunday = ₹1149
So, the plumber earned ₹1149 on Sunday.
| Period | Number of Days | Average Earning (₹) | Total Earning (₹) |
|---|---|---|---|
| Monday - Wednesday | 3 | 580 | $580 \times 3 = 1740$ |
| Thursday - Saturday | 3 | 612 | $612 \times 3 = 1836$ |
| Monday - Saturday | 6 | - | $1740 + 1836 = 3576$ |
| Monday - Sunday | 7 | 675 | $675 \times 7 = 4725$ |
| Sunday | 1 | - | $4725 - 3576 = 1149$ |
Conclusion on Plumber's Daily Earning
By breaking down the week's earnings into segments and using the given average figures, we calculated the total earnings for each period. Subtracting the total earnings for Monday to Saturday from the total earnings for the entire week allowed us to isolate the earning specifically for Sunday. The calculated earning on Sunday is ₹1149.
Revision Table: Average Earning Concepts
| Concept | Definition | Formula | Use Case in this Problem |
|---|---|---|---|
| Average | The sum of a set of values divided by the number of values in the set. It represents a typical value. | $\frac{\text{Sum of Values}}{\text{Number of Values}}$ | Given for different periods (Mon-Wed, Thu-Sat, Mon-Sun). |
| Total Sum | The sum of all values in a set. | Average $\times$ Number of Values | Calculated for Mon-Wed, Thu-Sat, and Mon-Sun to find daily earnings sums. |
| Difference | The result of subtracting one number from another. | Value1 - Value2 | Used to find the single day's earning (Sunday) by subtracting the 6-day total from the 7-day total. |
Additional Information: Understanding Averages and Total Sums
Understanding the relationship between average, total sum, and the number of items is fundamental in many quantitative problems. The average gives us a sense of the typical value, but the total sum gives us the complete amount over a period or set of items.
- If you know the average and the number of items, you can always find the total sum. This is what we did multiple times in this problem (e.g., finding total earning for Mon-Wed).
- If you know the total sum and the number of items, you can find the average.
- If you have the total sums for overlapping or consecutive periods, you can find the sum for the combined period or isolate the sum for a specific part (like finding Sunday's earning).
These types of problems involving averages over different time periods are common in aptitude tests and help assess one's ability to manipulate data and apply basic mathematical formulas.
Important Questions from Average
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