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Ramesh can complete a work in 15 days and along with Geeta, he completes the same work in 6 days. If Geeta along with Rajan takes 9 days to complete the same work, time taken by Rajan alone to complete the same work is …….. days.
- a)50
- b)75
- c)85
- d)90
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
Ramesh can complete a work in 15 days and along with Geeta, he complet...
Time taken by Rajan and Geeta to complete the work = 6 days
As we know, work is directly proportional to time, w/t = constant
Time taken by Ramesh to complete work = 15 days
According to the question,
1/15 + 1/x = 1/6
1/15 + 1/x = 1/6
Where x = time taken by Geeta to complete the same work,
⇒ 1/x = 1/6 – 1/15
⇒ x = 10 days
⇒ 1/x = 1/6 – 1/15
⇒ x = 10 days
For finding the efficiency of Rajan,
1/10 + 1/y = 1/9
1/10 + 1/y = 1/9
Where, y = time taken by Rajan alone to complete the same work,
⇒ 1/y = 1/9 – 1/10
⇒ 1/y = 1/90
∴ y = work efficiency of Rajan = 90 days
⇒ 1/y = 1/9 – 1/10
⇒ 1/y = 1/90
∴ y = work efficiency of Rajan = 90 days
Most Upvoted Answer
Ramesh can complete a work in 15 days and along with Geeta, he complet...
Understanding the Problem
To solve the problem, let's first determine the work rates of Ramesh, Geeta, and Rajan.
Ramesh's Work Rate
- Ramesh can complete the work in 15 days.
- His work rate = 1 work / 15 days = 1/15 work per day.
Combined Work Rate of Ramesh and Geeta
- Ramesh and Geeta together complete the work in 6 days.
- Their combined work rate = 1 work / 6 days = 1/6 work per day.
- Let Geeta's work rate be represented as G.
- Thus, Ramesh's work rate + Geeta's work rate = 1/15 + G = 1/6.
Finding Geeta's Work Rate
- Rearranging the equation: G = 1/6 - 1/15.
- Finding a common denominator (30):
- G = 5/30 - 2/30 = 3/30 = 1/10 work per day.
Geeta's Work Rate
- Geeta can complete the work in 10 days.
Combined Work Rate of Geeta and Rajan
- Geeta and Rajan together take 9 days to complete the work.
- Their combined work rate = 1 work / 9 days = 1/9 work per day.
- Let Rajan's work rate be represented as R.
- Thus, Geeta's work rate + Rajan's work rate = 1/10 + R = 1/9.
Finding Rajan's Work Rate
- Rearranging the equation: R = 1/9 - 1/10.
- Finding a common denominator (90):
- R = 10/90 - 9/90 = 1/90 work per day.
Calculating Rajan's Time Alone
- If Rajan's work rate is 1/90 work per day, then the time taken by Rajan alone to complete the work is:
- Time = 1 work / (1/90) = 90 days.
Conclusion
The time taken by Rajan alone to complete the same work is 90 days, which corresponds to option 'D'.
To solve the problem, let's first determine the work rates of Ramesh, Geeta, and Rajan.
Ramesh's Work Rate
- Ramesh can complete the work in 15 days.
- His work rate = 1 work / 15 days = 1/15 work per day.
Combined Work Rate of Ramesh and Geeta
- Ramesh and Geeta together complete the work in 6 days.
- Their combined work rate = 1 work / 6 days = 1/6 work per day.
- Let Geeta's work rate be represented as G.
- Thus, Ramesh's work rate + Geeta's work rate = 1/15 + G = 1/6.
Finding Geeta's Work Rate
- Rearranging the equation: G = 1/6 - 1/15.
- Finding a common denominator (30):
- G = 5/30 - 2/30 = 3/30 = 1/10 work per day.
Geeta's Work Rate
- Geeta can complete the work in 10 days.
Combined Work Rate of Geeta and Rajan
- Geeta and Rajan together take 9 days to complete the work.
- Their combined work rate = 1 work / 9 days = 1/9 work per day.
- Let Rajan's work rate be represented as R.
- Thus, Geeta's work rate + Rajan's work rate = 1/10 + R = 1/9.
Finding Rajan's Work Rate
- Rearranging the equation: R = 1/9 - 1/10.
- Finding a common denominator (90):
- R = 10/90 - 9/90 = 1/90 work per day.
Calculating Rajan's Time Alone
- If Rajan's work rate is 1/90 work per day, then the time taken by Rajan alone to complete the work is:
- Time = 1 work / (1/90) = 90 days.
Conclusion
The time taken by Rajan alone to complete the same work is 90 days, which corresponds to option 'D'.
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Ramesh can complete a work in 15 days and along with Geeta, he completes the same work in 6 days. If Geeta along with Rajan takes 9 days to complete the same work, time taken by Rajan alone to complete the same work is …….. days.a)50b)75c)85d)90Correct answer is option 'D'. Can you explain this answer?
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Ramesh can complete a work in 15 days and along with Geeta, he completes the same work in 6 days. If Geeta along with Rajan takes 9 days to complete the same work, time taken by Rajan alone to complete the same work is …….. days.a)50b)75c)85d)90Correct answer is option 'D'. Can you explain this answer? for SSC CHSL 2025 is part of SSC CHSL preparation. The Question and answers have been prepared according to the SSC CHSL exam syllabus. Information about Ramesh can complete a work in 15 days and along with Geeta, he completes the same work in 6 days. If Geeta along with Rajan takes 9 days to complete the same work, time taken by Rajan alone to complete the same work is …….. days.a)50b)75c)85d)90Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ramesh can complete a work in 15 days and along with Geeta, he completes the same work in 6 days. If Geeta along with Rajan takes 9 days to complete the same work, time taken by Rajan alone to complete the same work is …….. days.a)50b)75c)85d)90Correct answer is option 'D'. Can you explain this answer?.
Ramesh can complete a work in 15 days and along with Geeta, he completes the same work in 6 days. If Geeta along with Rajan takes 9 days to complete the same work, time taken by Rajan alone to complete the same work is …….. days.a)50b)75c)85d)90Correct answer is option 'D'. Can you explain this answer? for SSC CHSL 2025 is part of SSC CHSL preparation. The Question and answers have been prepared according to the SSC CHSL exam syllabus. Information about Ramesh can complete a work in 15 days and along with Geeta, he completes the same work in 6 days. If Geeta along with Rajan takes 9 days to complete the same work, time taken by Rajan alone to complete the same work is …….. days.a)50b)75c)85d)90Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ramesh can complete a work in 15 days and along with Geeta, he completes the same work in 6 days. If Geeta along with Rajan takes 9 days to complete the same work, time taken by Rajan alone to complete the same work is …….. days.a)50b)75c)85d)90Correct answer is option 'D'. Can you explain this answer?.
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