If you happen to be viewing the article Kaushalya can do a work in 20 days, while Kaikeyi can do the same work in 25 days. They started the work jointly. Few days later Sumitra also joined them and thus all of them completed the whole work in 10 days. All of them were paid total Rs.700. What is the share of Sumitra? ? on the website Math Hello Kitty, there are a couple of convenient ways for you to navigate through the content. You have the option to simply scroll down and leisurely read each section at your own pace. Alternatively, if you’re in a rush or looking for specific information, you can swiftly click on the table of contents provided. This will instantly direct you to the exact section that contains the information you need most urgently.
Find out how much money Sumitra gets after completing a job with Kaushalya and Kaikeyi in 10 days and getting paid a total of Rs. 700.
Kaushalya can do a work in 20 days, while Kaikeyi can do the same work in 25 days. They started the work jointly. Few days later Sumitra also joined them and thus all of them completed the whole work in 10 days. All of them were paid total Rs.700. What is the share of Sumitra?
Sumitra’s share is Rs.70
Here’s why
Let’s first find out the individual rates at which Kaushalya and Kaikeyi work per day.
Kaushalya’s rate = 1/20 (she completes 1 work in 20 days)
Kaikeyi’s rate = 1/25 (she completes 1 work in 25 days)
Now, when they work together, their combined rate is the sum of their individual rates:
Combined rate = Kaushalya’s rate + Kaikeyi’s rate
= 1/20 + 1/25 = (5 + 4) / 100
= 9/100
This means together they complete 9/100 of the work per day.
Now, let’s denote Sumitra’s rate as S.
Given that all three completed the work in 10 days:
(9/100 + S) * 10 = 1
Now, let’s solve for S:
(9/100 + S) * 10 = 1
90/100 + 10S = 1
10S = 1 – 90/100
10S = 10/100
S = 1/100
So, Sumitra’s rate is 1/100.
Now, let’s find Sumitra’s share of the total payment. Since they all worked for 10 days and Sumitra’s rate is 1/100, her share of the total payment is: Sumitra’s share = (1/100) * 10 * Total payment = (1/100) * 10 * 700 = 70
Therefore, Sumitra’s share of the payment is Rs. 70.
Time and Work in Mathematics
Time and work is a fundamental concept in mathematics that deals with the relationship between the amount of work that needs to be done, the rate at which it is done, and the time it takes to complete it. It is a crucial topic in various competitive exams and has practical applications in many real-world scenarios.
Here are the key concepts of time and work in mathematics:
1. Rate of Work:
- The rate of work is the amount of work done per unit of time. It is measured in units of work per unit of time, such as pages painted per hour, widgets produced per minute, or meters dug per day.
- The rate of work is inversely proportional to the time taken to complete the work. This means that if the rate of work increases, the time taken to complete the work decreases, and vice versa.
2. Work Done:
- The work done is the total amount of work completed. It is measured in the same units as the individual units of work, such as the total number of pages painted, the total number of widgets produced, or the total distance dug.
- The work done is directly proportional to the rate of work and the time taken. This means that if either the rate of work or the time taken increases, the work done also increases.
3. Important Formulas:
- Work Done = Rate of Work × Time Taken
- Rate of Work = Work Done / Time Taken
- Time Taken = Work Done / Rate of Work
4. Applications:
- Time and work problems have numerous applications in various fields, including construction, manufacturing, logistics, and personal finance.
- They can be used to calculate things like:
- How long it will take to complete a project with a given number of workers.
- How many workers are needed to complete a project in a specific amount of time.
- The cost of labor for a project based on the rate of pay and the time taken.
Examples:
- A painter can paint 10 pages per hour. How long will it take her to paint 50 pages?
- A factory produces 20 widgets per hour. How many widgets will it produce in 8 hours?
- A worker can dig a trench at a rate of 2 meters per day. How long will it take him to dig a trench 10 meters long?
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Source: Math Hello Kitty
Categories: Math
