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If A can do a work in 10 days while B can do the same work in 15 days. They began to work together, but A left 2 days before its completion. In what time is the work finished?
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If A can do a work in 10 days while B can do the same work in 15 days....
Work Rates of A and B
A can complete the work in 10 days, while B can finish it in 15 days. To find their work rates:
- A's work rate = \( \frac{1}{10} \) of the work per day.
- B's work rate = \( \frac{1}{15} \) of the work per day.
Total Work Rate Together
When A and B work together, their combined work rate is:
- Combined work rate = \( \frac{1}{10} + \frac{1}{15} \)
To calculate this, find a common denominator (30):
- \( \frac{3}{30} + \frac{2}{30} = \frac{5}{30} = \frac{1}{6} \)
Thus, together they can complete \( \frac{1}{6} \) of the work in one day.
Work Done Before A Leaves
Let the total time they work together be \( x \) days. A leaves 2 days before the work is completed, which means B works alone for 2 days. Hence, they worked together for \( x - 2 \) days.
The total work done can be expressed as:
- Work done by A and B together = \( (x - 2) \times \frac{1}{6} \)
- Work done by B alone for 2 days = \( 2 \times \frac{1}{15} \)
The equation becomes:
\[ (x - 2) \times \frac{1}{6} + 2 \times \frac{1}{15} = 1 \]
Solve the Equation
This can be simplified:
1. Multiply through by 30 (LCM of 6 and 15):
\[ 5(x - 2) + 4 = 30 \]
2. Rearranging gives:
\[ 5x - 10 + 4 = 30 \]
\[ 5x - 6 = 30 \]
\[ 5x = 36 \]
\[ x = 7.2 \]
Final Time Calculation
Thus, the total time taken to complete the work:
- Total time = \( 7.2 \) days
In conclusion, the work is finished in **7.2 days**.
A can complete the work in 10 days, while B can finish it in 15 days. To find their work rates:
- A's work rate = \( \frac{1}{10} \) of the work per day.
- B's work rate = \( \frac{1}{15} \) of the work per day.
Total Work Rate Together
When A and B work together, their combined work rate is:
- Combined work rate = \( \frac{1}{10} + \frac{1}{15} \)
To calculate this, find a common denominator (30):
- \( \frac{3}{30} + \frac{2}{30} = \frac{5}{30} = \frac{1}{6} \)
Thus, together they can complete \( \frac{1}{6} \) of the work in one day.
Work Done Before A Leaves
Let the total time they work together be \( x \) days. A leaves 2 days before the work is completed, which means B works alone for 2 days. Hence, they worked together for \( x - 2 \) days.
The total work done can be expressed as:
- Work done by A and B together = \( (x - 2) \times \frac{1}{6} \)
- Work done by B alone for 2 days = \( 2 \times \frac{1}{15} \)
The equation becomes:
\[ (x - 2) \times \frac{1}{6} + 2 \times \frac{1}{15} = 1 \]
Solve the Equation
This can be simplified:
1. Multiply through by 30 (LCM of 6 and 15):
\[ 5(x - 2) + 4 = 30 \]
2. Rearranging gives:
\[ 5x - 10 + 4 = 30 \]
\[ 5x - 6 = 30 \]
\[ 5x = 36 \]
\[ x = 7.2 \]
Final Time Calculation
Thus, the total time taken to complete the work:
- Total time = \( 7.2 \) days
In conclusion, the work is finished in **7.2 days**.
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If A can do a work in 10 days while B can do the same work in 15 days. They began to work together, but A left 2 days before its completion. In what time is the work finished?
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If A can do a work in 10 days while B can do the same work in 15 days. They began to work together, but A left 2 days before its completion. In what time is the work finished? 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 If A can do a work in 10 days while B can do the same work in 15 days. They began to work together, but A left 2 days before its completion. In what time is the work finished? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A can do a work in 10 days while B can do the same work in 15 days. They began to work together, but A left 2 days before its completion. In what time is the work finished?.
If A can do a work in 10 days while B can do the same work in 15 days. They began to work together, but A left 2 days before its completion. In what time is the work finished? 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 If A can do a work in 10 days while B can do the same work in 15 days. They began to work together, but A left 2 days before its completion. In what time is the work finished? covers all topics & solutions for SSC CHSL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If A can do a work in 10 days while B can do the same work in 15 days. They began to work together, but A left 2 days before its completion. In what time is the work finished?.
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