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A does half as much work as B in three-fourth of the time. If they together can complete a work in 18 days, find how long B alone would take to do the work?
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A does half as much work as B in three-fourth of the time. If they tog...
Understanding the Problem
To solve the problem, let's define the work done by A and B, and their respective working rates.
Work Relationship
- Let the amount of work that B can complete in one day be represented as \( b \).
- Therefore, A does half as much work as B in three-fourths of the time. So, A's work rate is:
- \( a = \frac{1}{2}b \) (since A does half the work of B)
Using the time relation, if B completes work in \( t_B \) days, then A completes it in \( \frac{3}{4}t_B \) days.
Combined Work Rate
- The total work can be expressed as:
- \( W = b \times t_B \) for B
- \( W = a \times \frac{3}{4}t_B = \frac{1}{2}b \times \frac{3}{4}t_B = \frac{3}{8}bt_B \) for A
Since they can complete the work together in 18 days:
- The combined work rate:
- \( a + b = \frac{3}{8}b + b = \frac{11}{8}b \)
Thus, the total work done together in 18 days is:
- \( 18 \times \frac{11}{8}b = W \)
Finding B's Time Alone
We already established that:
- \( W = b \times t_B \)
Setting the equal expressions for work:
- \( 18 \times \frac{11}{8}b = b \times t_B \)
By cancelling \( b \) from both sides (assuming \( b \neq 0 \)):
- \( t_B = \frac{18 \times 11}{8} \)
- \( t_B = 24.75 \) days
Conclusion
Thus, B alone would take approximately **24.75 days** to complete the work.
To solve the problem, let's define the work done by A and B, and their respective working rates.
Work Relationship
- Let the amount of work that B can complete in one day be represented as \( b \).
- Therefore, A does half as much work as B in three-fourths of the time. So, A's work rate is:
- \( a = \frac{1}{2}b \) (since A does half the work of B)
Using the time relation, if B completes work in \( t_B \) days, then A completes it in \( \frac{3}{4}t_B \) days.
Combined Work Rate
- The total work can be expressed as:
- \( W = b \times t_B \) for B
- \( W = a \times \frac{3}{4}t_B = \frac{1}{2}b \times \frac{3}{4}t_B = \frac{3}{8}bt_B \) for A
Since they can complete the work together in 18 days:
- The combined work rate:
- \( a + b = \frac{3}{8}b + b = \frac{11}{8}b \)
Thus, the total work done together in 18 days is:
- \( 18 \times \frac{11}{8}b = W \)
Finding B's Time Alone
We already established that:
- \( W = b \times t_B \)
Setting the equal expressions for work:
- \( 18 \times \frac{11}{8}b = b \times t_B \)
By cancelling \( b \) from both sides (assuming \( b \neq 0 \)):
- \( t_B = \frac{18 \times 11}{8} \)
- \( t_B = 24.75 \) days
Conclusion
Thus, B alone would take approximately **24.75 days** to complete the work.
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A does half as much work as B in three-fourth of the time. If they together can complete a work in 18 days, find how long B alone would take to do the work?
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A does half as much work as B in three-fourth of the time. If they together can complete a work in 18 days, find how long B alone would take to do 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 does half as much work as B in three-fourth of the time. If they together can complete a work in 18 days, find how long B alone would take to do the work? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A does half as much work as B in three-fourth of the time. If they together can complete a work in 18 days, find how long B alone would take to do the work?.
A does half as much work as B in three-fourth of the time. If they together can complete a work in 18 days, find how long B alone would take to do 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 does half as much work as B in three-fourth of the time. If they together can complete a work in 18 days, find how long B alone would take to do the work? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A does half as much work as B in three-fourth of the time. If they together can complete a work in 18 days, find how long B alone would take to do the work?.
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