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.
Important Questions from Data Interpretation
The table below shows the number of toys of 6 different colours sold from a shop during a given period. The table also shows the percentage of toys of each colour which are cars.
Colour Total toys Percentage of cars C1 500 12 C2 600 15 C3 400 12.5 C4 550 10 C5 650 20 C6 450 10 What is the total number of car toys of C2 and C3 taken together?
Study the given graph carefully and answer the question that follows. The graph shows the demand and production of different companies.
The ratio between the companies having more production than demand and more demand than production is:
Study the given table and answer the question that follows. The given table shows the number of new employees added to different categories of employees in a company for four years and the number of employees from these categories who left the company every year.
During the period between 2001 and 2004, the total number of Technicians who left the Company is what percentage (rounded off to the nearest integer) of the total number of Technicians who joined the Company?
The given pie-chart shows the percentage distribution of 20,000 employees in a company. Study the given chart and answer the question that follows. If 30% of the employees in department D are females, then how many male employees are there in that department?
The given pie chart shows the expenditure by a state government on various sports during a particular year. If the total amount spent on tennis and football is ₹1,45,000, then the total amount (in ₹) spent on all the given sports is:
