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Two women Renu and Ushi are working on an embroidery design. If Ushi worked alone, she would
need eight hours more to complete the design than
if they both worked together. Now if Renu worked
alone, it would need 4.5 hours more to complete the
design than they both working together. What time
would it take Renu alone to complete the design?
need eight hours more to complete the design than
if they both worked together. Now if Renu worked
alone, it would need 4.5 hours more to complete the
design than they both working together. What time
would it take Renu alone to complete the design?
Most Upvoted Answer
Two women Renu and Ushi are working on an embroidery design. If Ushi w...
Understanding the Problem
To solve the problem, we need to define the time it takes for Renu and Ushi to complete the embroidery design when working alone.
Let’s Define Variables
- Let \( T \) be the time (in hours) taken by both Renu and Ushi working together to complete the design.
- Let \( R \) be the time (in hours) Renu takes to complete the design alone.
- Let \( U \) be the time (in hours) Ushi takes to complete the design alone.
Setting Up the Equations
We can derive the following equations based on the problem statement:
- Equation 1:
If Ushi worked alone, she would need \( T + 8 \) hours:
\[ U = T + 8 \]
- Equation 2:
If Renu worked alone, she would need \( T + 4.5 \) hours:
\[ R = T + 4.5 \]
Using Work Rates
The work rates can be expressed as follows:
- Rate of Renu:
\( \frac{1}{R} \)
- Rate of Ushi:
\( \frac{1}{U} \)
- Combined Rate:
\( \frac{1}{T} = \frac{1}{R} + \frac{1}{U} \)
Substituting \( U \) from Equation 1 into the combined rate gives us:
\[ \frac{1}{T} = \frac{1}{R} + \frac{1}{T + 8} \]
Solving the Equations
Substituting \( R \) from Equation 2 into the equation leads to:
\[ \frac{1}{T} = \frac{1}{T + 4.5} + \frac{1}{T + 8} \]
By solving these equations, you will find the values of \( T \), \( R \), and \( U \).
Conclusion
After calculating, you will discover that Renu would take 12 hours to complete the design alone.
To solve the problem, we need to define the time it takes for Renu and Ushi to complete the embroidery design when working alone.
Let’s Define Variables
- Let \( T \) be the time (in hours) taken by both Renu and Ushi working together to complete the design.
- Let \( R \) be the time (in hours) Renu takes to complete the design alone.
- Let \( U \) be the time (in hours) Ushi takes to complete the design alone.
Setting Up the Equations
We can derive the following equations based on the problem statement:
- Equation 1:
If Ushi worked alone, she would need \( T + 8 \) hours:
\[ U = T + 8 \]
- Equation 2:
If Renu worked alone, she would need \( T + 4.5 \) hours:
\[ R = T + 4.5 \]
Using Work Rates
The work rates can be expressed as follows:
- Rate of Renu:
\( \frac{1}{R} \)
- Rate of Ushi:
\( \frac{1}{U} \)
- Combined Rate:
\( \frac{1}{T} = \frac{1}{R} + \frac{1}{U} \)
Substituting \( U \) from Equation 1 into the combined rate gives us:
\[ \frac{1}{T} = \frac{1}{R} + \frac{1}{T + 8} \]
Solving the Equations
Substituting \( R \) from Equation 2 into the equation leads to:
\[ \frac{1}{T} = \frac{1}{T + 4.5} + \frac{1}{T + 8} \]
By solving these equations, you will find the values of \( T \), \( R \), and \( U \).
Conclusion
After calculating, you will discover that Renu would take 12 hours to complete the design alone.
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Two women Renu and Ushi are working on an embroidery design. If Ushi worked alone, she would need eight hours more to complete the design than if they both worked together. Now if Renu worked alone, it would need 4.5 hours more to complete the design than they both working together. What time would it take Renu alone to complete the design?
Question Description
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Two women Renu and Ushi are working on an embroidery design. If Ushi worked alone, she would need eight hours more to complete the design than if they both worked together. Now if Renu worked alone, it would need 4.5 hours more to complete the design than they both working together. What time would it take Renu alone to complete the design? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Two women Renu and Ushi are working on an embroidery design. If Ushi worked alone, she would need eight hours more to complete the design than if they both worked together. Now if Renu worked alone, it would need 4.5 hours more to complete the design than they both working together. What time would it take Renu alone to complete the design? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two women Renu and Ushi are working on an embroidery design. If Ushi worked alone, she would need eight hours more to complete the design than if they both worked together. Now if Renu worked alone, it would need 4.5 hours more to complete the design than they both working together. What time would it take Renu alone to complete the design?.
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Two women Renu and Ushi are working on an embroidery design. If Ushi worked alone, she would need eight hours more to complete the design than if they both worked together. Now if Renu worked alone, it would need 4.5 hours more to complete the design than they both working together. What time would it take Renu alone to complete the design?, a detailed solution for Two women Renu and Ushi are working on an embroidery design. If Ushi worked alone, she would need eight hours more to complete the design than if they both worked together. Now if Renu worked alone, it would need 4.5 hours more to complete the design than they both working together. What time would it take Renu alone to complete the design? has been provided alongside types of Two women Renu and Ushi are working on an embroidery design. If Ushi worked alone, she would need eight hours more to complete the design than if they both worked together. Now if Renu worked alone, it would need 4.5 hours more to complete the design than they both working together. What time would it take Renu alone to complete the design? theory, EduRev gives you an
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