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A and B can do a piece of work in 45 days and 40 days respectively. They begin to do the work together but A left after some days and then B completed the remaining work in 23 days. The number of days, after which A left the work was.:?
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A and B can do a piece of work in 45 days and 40 days respectively. Th...
Work Rates of A and B
To solve the problem, we first need to determine the work rates of A and B.
- A can complete the work in 45 days, so A’s work rate is:
**Work rate of A = 1/45 work/day**
- B can complete the work in 40 days, so B’s work rate is:
**Work rate of B = 1/40 work/day**
Total Work Rate Together
When A and B work together, their combined work rate is:
- **Combined work rate = (1/45 + 1/40)**
To add these fractions, find a common denominator (which is 360):
- **Combined work rate = (8/360 + 9/360) = 17/360 work/day**
Work Done by A and B Together
Let’s say A worked with B for **x days**. The work done by both in x days will be:
- **Work done = x * (17/360)**
Remaining Work by B
After A leaves, B finishes the remaining work in 23 days. The work done by B in 23 days is:
- **Work done by B = 23 * (1/40) = 23/40**
The total work done is equal to 1 (the whole work):
- **Work done by A and B together + Work done by B alone = 1**
Substituting the equations gives:
- **(17x/360) + (23/40) = 1**
Solving the Equation
Now, we need to solve for x:
1. Convert 23/40 to a fraction with a denominator of 360:
**23/40 = 207/360**
2. Substitute and rearrange:
**(17x/360) + (207/360) = 1**
**17x + 207 = 360**
**17x = 153**
**x = 9**
Conclusion
A left the work after **9 days**. Thus, A and B worked together for 9 days before A departed, and B completed the remaining work alone in 23 days.
To solve the problem, we first need to determine the work rates of A and B.
- A can complete the work in 45 days, so A’s work rate is:
**Work rate of A = 1/45 work/day**
- B can complete the work in 40 days, so B’s work rate is:
**Work rate of B = 1/40 work/day**
Total Work Rate Together
When A and B work together, their combined work rate is:
- **Combined work rate = (1/45 + 1/40)**
To add these fractions, find a common denominator (which is 360):
- **Combined work rate = (8/360 + 9/360) = 17/360 work/day**
Work Done by A and B Together
Let’s say A worked with B for **x days**. The work done by both in x days will be:
- **Work done = x * (17/360)**
Remaining Work by B
After A leaves, B finishes the remaining work in 23 days. The work done by B in 23 days is:
- **Work done by B = 23 * (1/40) = 23/40**
The total work done is equal to 1 (the whole work):
- **Work done by A and B together + Work done by B alone = 1**
Substituting the equations gives:
- **(17x/360) + (23/40) = 1**
Solving the Equation
Now, we need to solve for x:
1. Convert 23/40 to a fraction with a denominator of 360:
**23/40 = 207/360**
2. Substitute and rearrange:
**(17x/360) + (207/360) = 1**
**17x + 207 = 360**
**17x = 153**
**x = 9**
Conclusion
A left the work after **9 days**. Thus, A and B worked together for 9 days before A departed, and B completed the remaining work alone in 23 days.
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A and B can do a piece of work in 45 days and 40 days respectively. They begin to do the work together but A left after some days and then B completed the remaining work in 23 days. The number of days, after which A left the work was.:?
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A and B can do a piece of work in 45 days and 40 days respectively. They begin to do the work together but A left after some days and then B completed the remaining work in 23 days. The number of days, after which A left the work was.:? 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 and B can do a piece of work in 45 days and 40 days respectively. They begin to do the work together but A left after some days and then B completed the remaining work in 23 days. The number of days, after which A left the work was.:? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A and B can do a piece of work in 45 days and 40 days respectively. They begin to do the work together but A left after some days and then B completed the remaining work in 23 days. The number of days, after which A left the work was.:?.
A and B can do a piece of work in 45 days and 40 days respectively. They begin to do the work together but A left after some days and then B completed the remaining work in 23 days. The number of days, after which A left the work was.:? 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 and B can do a piece of work in 45 days and 40 days respectively. They begin to do the work together but A left after some days and then B completed the remaining work in 23 days. The number of days, after which A left the work was.:? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A and B can do a piece of work in 45 days and 40 days respectively. They begin to do the work together but A left after some days and then B completed the remaining work in 23 days. The number of days, after which A left the work was.:?.
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