The table given below shows the earnings of two persons on five different days. Earnings Days P Q Monday 105 150 Tuesday 96 110 Wednesday 65 122 Thursday 115 106 Friday 130 68
Calculating Total Earnings Ratio from Table Data
The problem requires us to calculate the total earnings for two persons, P and Q, over five different days and then find the ratio of P's total earnings to Q's total earnings.
Understanding the Given Data Table
The data is presented in a table showing the daily earnings for both P and Q for Monday through Friday.
| Days | Earnings P | Earnings Q |
|---|---|---|
| Monday | 105 | 150 |
| Tuesday | 96 | 110 |
| Wednesday | 65 | 122 |
| Thursday | 115 | 106 |
| Friday | 130 | 68 |
Calculating Total Earnings for Person P
To find the total earnings of P, we sum up P's earnings for each of the five days:
Total Earnings of P = Earnings on Monday + Tuesday + Wednesday + Thursday + Friday
Total Earnings of P $= 105 + 96 + 65 + 115 + 130$
Total Earnings of P $= 201 + 65 + 115 + 130$
Total Earnings of P $= 266 + 115 + 130$
Total Earnings of P $= 381 + 130$
Total Earnings of P $= 511$
So, the total earnings of person P over the five days is 511.
Calculating Total Earnings for Person Q
Similarly, to find the total earnings of Q, we sum up Q's earnings for each of the five days:
Total Earnings of Q = Earnings on Monday + Tuesday + Wednesday + Thursday + Friday
Total Earnings of Q $= 150 + 110 + 122 + 106 + 68$
Total Earnings of Q $= 260 + 122 + 106 + 68$
Total Earnings of Q $= 382 + 106 + 68$
Total Earnings of Q $= 488 + 68$
Total Earnings of Q $= 556$
So, the total earnings of person Q over the five days is 556.
Finding the Ratio of Total Earnings of P to Q
The ratio of the total earnings of P to the total earnings of Q is given by:
Ratio $= \frac{\text{Total Earnings of P}}{\text{Total Earnings of Q}}$
Ratio $= \frac{511}{556}$
This can be written as the ratio $511 : 556$. We check if this ratio can be simplified by finding a common factor for 511 and 556. 511 is not divisible by 2, 3, 5. We can try prime numbers. Let's check 7 (511/7 = 73), 11, 13, 17, 19 (511/19=26.8), 23 (511/23=22.2), etc. 511 = $7 \times 73$. Now check if 556 is divisible by 7 or 73. $556 \div 7 \approx 79.4$, $556 \div 73 \approx 7.6$. So, 511 and 556 do not have common factors other than 1. Thus, the ratio $511 : 556$ is in its simplest form.
Therefore, the ratio of the total earnings of P to the total earnings of Q is $511 : 556$.
Revision Table: Earnings Ratio Calculation
- Identify the data needed: Daily earnings for P and Q.
- Calculate the sum of daily earnings for P.
- Calculate the sum of daily earnings for Q.
- Form the ratio of P's total earnings to Q's total earnings.
- Simplify the ratio if possible.
Additional Information: Understanding Ratios and Tables
A ratio is a comparison of two quantities by division. It shows how many times one quantity is contained within another. Ratios are often used to compare different values derived from data, such as total earnings or performance metrics.
Tables are a structured way to organize and display data. Each row and column represents specific information, making it easier to read and analyze data points like daily earnings for multiple individuals over a period.
To calculate a ratio from a table:
- Identify the specific values you need to compare (e.g., total earnings of P and Q).
- Perform any necessary calculations (e.g., sum up daily earnings to get total earnings).
- Write the ratio in the form of A:B or A/B, where A is the first quantity and B is the second quantity in the comparison.
- Simplify the ratio by dividing both parts by their greatest common divisor if required.
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Category
2010
2011
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9000
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Year
Type I
Type II
Type III
Type IV
Type V
2006
75
144
114
102
108
2007
90
126
102
84
126
2008
96
114
75
105
135
2009
105
90
150
90
75
2010
90
75
135
75
90
2011
105
60
165
45
120
2012
115
85
160
100
145
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A
D
B
G
E
C
F
