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Rachna can finish a work in 16 days and perina can do the same work in half the time taken by Rachna. Then, working together , what part of the same work they can finish in a day?
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Rachna can finish a work in 16 days and perina can do the same work in...
Understanding the Problem
To solve the problem, we first need to determine the work rates of Rachna and Perina.
Work Rate of Rachna
- Rachna can complete the work in 16 days.
- Therefore, her work rate is:
- 1 work unit / 16 days = 1/16 of the work per day.
Work Rate of Perina
- Perina completes the same work in half the time taken by Rachna.
- Since Rachna takes 16 days, Perina takes:
- 16 days / 2 = 8 days.
- Hence, Perina's work rate is:
- 1 work unit / 8 days = 1/8 of the work per day.
Combined Work Rate
Now, we will calculate their combined work rate when Rachna and Perina work together.
- Combined work rate = Rachna's work rate + Perina's work rate
- Combined work rate = (1/16 + 1/8)
Finding a Common Denominator
To add these fractions, we need a common denominator:
- The least common multiple of 16 and 8 is 16.
- Convert 1/8 to a fraction with a denominator of 16:
- 1/8 = 2/16
Calculating Combined Rate
- Now add the two fractions:
- 1/16 + 2/16 = 3/16
Conclusion
Thus, when working together, Rachna and Perina can finish:
- 3/16 of the work in one day.
This means that together, they are efficient and can complete a significant portion of the task in a short amount of time.
To solve the problem, we first need to determine the work rates of Rachna and Perina.
Work Rate of Rachna
- Rachna can complete the work in 16 days.
- Therefore, her work rate is:
- 1 work unit / 16 days = 1/16 of the work per day.
Work Rate of Perina
- Perina completes the same work in half the time taken by Rachna.
- Since Rachna takes 16 days, Perina takes:
- 16 days / 2 = 8 days.
- Hence, Perina's work rate is:
- 1 work unit / 8 days = 1/8 of the work per day.
Combined Work Rate
Now, we will calculate their combined work rate when Rachna and Perina work together.
- Combined work rate = Rachna's work rate + Perina's work rate
- Combined work rate = (1/16 + 1/8)
Finding a Common Denominator
To add these fractions, we need a common denominator:
- The least common multiple of 16 and 8 is 16.
- Convert 1/8 to a fraction with a denominator of 16:
- 1/8 = 2/16
Calculating Combined Rate
- Now add the two fractions:
- 1/16 + 2/16 = 3/16
Conclusion
Thus, when working together, Rachna and Perina can finish:
- 3/16 of the work in one day.
This means that together, they are efficient and can complete a significant portion of the task in a short amount of time.
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Rachna can finish a work in 16 days and perina can do the same work in half the time taken by Rachna. Then, working together , what part of the same work they can finish in a day?
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Rachna can finish a work in 16 days and perina can do the same work in half the time taken by Rachna. Then, working together , what part of the same work they can finish in a day? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Rachna can finish a work in 16 days and perina can do the same work in half the time taken by Rachna. Then, working together , what part of the same work they can finish in a day? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Rachna can finish a work in 16 days and perina can do the same work in half the time taken by Rachna. Then, working together , what part of the same work they can finish in a day?.
Rachna can finish a work in 16 days and perina can do the same work in half the time taken by Rachna. Then, working together , what part of the same work they can finish in a day? for Class 8 2024 is part of Class 8 preparation. The Question and answers have been prepared according to the Class 8 exam syllabus. Information about Rachna can finish a work in 16 days and perina can do the same work in half the time taken by Rachna. Then, working together , what part of the same work they can finish in a day? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Rachna can finish a work in 16 days and perina can do the same work in half the time taken by Rachna. Then, working together , what part of the same work they can finish in a day?.
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