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A can do a piece of work in 15 days and B in 20 days. With the help of C, they. finish the work in 5 days. How long will it take C to finish the work?
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A can do a piece of work in 15 days and B in 20 days. With the help of...
Understanding the Work Rates
A can complete the work in 15 days, so A's work rate is:
- A's work rate = 1/15 of the work per day.
B can finish the work in 20 days, thus B's work rate is:
- B's work rate = 1/20 of the work per day.
Combined Work Rate of A and B
To find the combined work rate of A and B:
- Combined work rate = A's work rate + B's work rate
- Combined work rate = 1/15 + 1/20
To add these fractions, we need a common denominator:
- LCM of 15 and 20 is 60.
- A's rate = 4/60
- B's rate = 3/60
So,
- Combined work rate = 4/60 + 3/60 = 7/60 of the work per day.
Involvement of C
With the help of C, A and B finish the work in 5 days:
- Total work done in 5 days = 1 (complete work)
Using the combined work rate:
- (7/60 + C's work rate) × 5 = 1
- 7/60 × 5 + C's work rate × 5 = 1
- 35/60 + C's work rate × 5 = 1
- C's work rate × 5 = 1 - 35/60
- C's work rate × 5 = 25/60
- C's work rate = 25/(60 × 5) = 1/12 of the work per day.
Time Taken by C Alone
To find how long it will take for C to finish the work alone:
- If C's work rate = 1/12, then C will take:
- Time = 1 / (1/12) = 12 days.
Conclusion
Thus, C will take **12 days** to finish the work alone.
A can complete the work in 15 days, so A's work rate is:
- A's work rate = 1/15 of the work per day.
B can finish the work in 20 days, thus B's work rate is:
- B's work rate = 1/20 of the work per day.
Combined Work Rate of A and B
To find the combined work rate of A and B:
- Combined work rate = A's work rate + B's work rate
- Combined work rate = 1/15 + 1/20
To add these fractions, we need a common denominator:
- LCM of 15 and 20 is 60.
- A's rate = 4/60
- B's rate = 3/60
So,
- Combined work rate = 4/60 + 3/60 = 7/60 of the work per day.
Involvement of C
With the help of C, A and B finish the work in 5 days:
- Total work done in 5 days = 1 (complete work)
Using the combined work rate:
- (7/60 + C's work rate) × 5 = 1
- 7/60 × 5 + C's work rate × 5 = 1
- 35/60 + C's work rate × 5 = 1
- C's work rate × 5 = 1 - 35/60
- C's work rate × 5 = 25/60
- C's work rate = 25/(60 × 5) = 1/12 of the work per day.
Time Taken by C Alone
To find how long it will take for C to finish the work alone:
- If C's work rate = 1/12, then C will take:
- Time = 1 / (1/12) = 12 days.
Conclusion
Thus, C will take **12 days** to finish the work alone.
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A can do a piece of work in 15 days and B in 20 days. With the help of C, they. finish the work in 5 days. How long will it take C to finish the work?
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A can do a piece of work in 15 days and B in 20 days. With the help of C, they. finish the work in 5 days. How long will it take C to finish the work? 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 A can do a piece of work in 15 days and B in 20 days. With the help of C, they. finish the work in 5 days. How long will it take C to finish the work? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A can do a piece of work in 15 days and B in 20 days. With the help of C, they. finish the work in 5 days. How long will it take C to finish the work?.
A can do a piece of work in 15 days and B in 20 days. With the help of C, they. finish the work in 5 days. How long will it take C to finish the work? 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 A can do a piece of work in 15 days and B in 20 days. With the help of C, they. finish the work in 5 days. How long will it take C to finish the work? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A can do a piece of work in 15 days and B in 20 days. With the help of C, they. finish the work in 5 days. How long will it take C to finish the work?.
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