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A, B and C can do this a piece of work in four days. A alone can do the same work in 12 days and B alone can do the same work in 10 days. How long will C take to do the work alone?
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A, B and C can do this a piece of work in four days. A alone can do th...
Understanding the Problem
To find out how long C will take to complete the work alone, we first need to calculate the work rates of A, B, and C together and then determine C's individual work rate.
Work Rates of A and B
- A can complete the work in 12 days, so A's work rate is:
- Work done by A in one day = 1/12
- B can complete the work in 10 days, so B's work rate is:
- Work done by B in one day = 1/10
Combined Work Rate of A, B, and C
- A, B, and C together can finish the work in 4 days, thus their combined work rate is:
- Work done by A, B, and C in one day = 1/4
Calculating C's Work Rate
- Now, we can find C's work rate by using the combined work rate:
- C's work rate = Combined work rate - (A's work rate + B's work rate)
- Plugging in the values:
- C's work rate = 1/4 - (1/12 + 1/10)
Finding a Common Denominator
- To subtract these fractions, we need a common denominator, which is 60:
- 1/12 = 5/60
- 1/10 = 6/60
- So, A's and B's combined work rate = 5/60 + 6/60 = 11/60
Final Calculation for C's Work Rate
- Now, substituting back:
- C's work rate = 1/4 - 11/60
- C's work rate = 15/60 - 11/60 = 4/60 = 1/15
Time Taken by C Alone
- The time taken by C to complete the work alone is the reciprocal of C's work rate:
- C's time = 1/(1/15) = 15 days
Thus, C will take 15 days to complete the work alone.
To find out how long C will take to complete the work alone, we first need to calculate the work rates of A, B, and C together and then determine C's individual work rate.
Work Rates of A and B
- A can complete the work in 12 days, so A's work rate is:
- Work done by A in one day = 1/12
- B can complete the work in 10 days, so B's work rate is:
- Work done by B in one day = 1/10
Combined Work Rate of A, B, and C
- A, B, and C together can finish the work in 4 days, thus their combined work rate is:
- Work done by A, B, and C in one day = 1/4
Calculating C's Work Rate
- Now, we can find C's work rate by using the combined work rate:
- C's work rate = Combined work rate - (A's work rate + B's work rate)
- Plugging in the values:
- C's work rate = 1/4 - (1/12 + 1/10)
Finding a Common Denominator
- To subtract these fractions, we need a common denominator, which is 60:
- 1/12 = 5/60
- 1/10 = 6/60
- So, A's and B's combined work rate = 5/60 + 6/60 = 11/60
Final Calculation for C's Work Rate
- Now, substituting back:
- C's work rate = 1/4 - 11/60
- C's work rate = 15/60 - 11/60 = 4/60 = 1/15
Time Taken by C Alone
- The time taken by C to complete the work alone is the reciprocal of C's work rate:
- C's time = 1/(1/15) = 15 days
Thus, C will take 15 days to complete the work alone.
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A, B and C can do this a piece of work in four days. A alone can do the same work in 12 days and B alone can do the same work in 10 days. How long will C take to do the work alone?
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A, B and C can do this a piece of work in four days. A alone can do the same work in 12 days and B alone can do the same work in 10 days. How long will C take to do the work alone? 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 A, B and C can do this a piece of work in four days. A alone can do the same work in 12 days and B alone can do the same work in 10 days. How long will C take to do the work alone? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A, B and C can do this a piece of work in four days. A alone can do the same work in 12 days and B alone can do the same work in 10 days. How long will C take to do the work alone?.
A, B and C can do this a piece of work in four days. A alone can do the same work in 12 days and B alone can do the same work in 10 days. How long will C take to do the work alone? 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 A, B and C can do this a piece of work in four days. A alone can do the same work in 12 days and B alone can do the same work in 10 days. How long will C take to do the work alone? covers all topics & solutions for Class 8 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A, B and C can do this a piece of work in four days. A alone can do the same work in 12 days and B alone can do the same work in 10 days. How long will C take to do the work alone?.
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