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A can do a piece of work in 18 days, B in 36 days and C in 72 days. All begin to do it together but A leaves after 8 days and B leaves 7 days before the completion of the work. The total number of days they worked for is
- a)20 days
- b)18 days
- c)16 days
- d)24 days
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A can do a piece of work in 18 days, B in 36 days and C in 72 days. Al...
Given,
A can do a piece of work in 18 days
∴ Part of work done by A in 1 day = 1/18
B can do a piece of work in 36days
∴ Part of work done by B in 1 day = 1/36
C can do a piece of work in 72 days
∴ Part of work done by C in 1 day = 1/72
Let,
Total number of days they work = x days
Number of days A work = 8 days
∵ B leaves7 days before the completion of the work
Number of days B work = (x – 7) days
And, Number of days C work= x days
∴ {(1/18) × 8 } + {(1/36) × (x – 7)} + {(1/72) × x} = 1
⇒ 4/9 + (x – 7)/36 + x/72 = 1
⇒ (32 + 2x -14 + x)/72 = 1
⇒ 18 + 3x = 72
⇒ 3x = 54
⇒ x = 18 days
A can do a piece of work in 18 days
∴ Part of work done by A in 1 day = 1/18
B can do a piece of work in 36days
∴ Part of work done by B in 1 day = 1/36
C can do a piece of work in 72 days
∴ Part of work done by C in 1 day = 1/72
Let,
Total number of days they work = x days
Number of days A work = 8 days
∵ B leaves7 days before the completion of the work
Number of days B work = (x – 7) days
And, Number of days C work= x days
∴ {(1/18) × 8 } + {(1/36) × (x – 7)} + {(1/72) × x} = 1
⇒ 4/9 + (x – 7)/36 + x/72 = 1
⇒ (32 + 2x -14 + x)/72 = 1
⇒ 18 + 3x = 72
⇒ 3x = 54
⇒ x = 18 days
Most Upvoted Answer
A can do a piece of work in 18 days, B in 36 days and C in 72 days. Al...
Understanding the Work Rates
- A can complete the work in 18 days, so A's work rate is \( \frac{1}{18} \) of the work per day.
- B can complete the work in 36 days, so B's work rate is \( \frac{1}{36} \) of the work per day.
- C can complete the work in 72 days, so C's work rate is \( \frac{1}{72} \) of the work per day.
Calculating Combined Work Rate
- The combined work rate of A, B, and C when working together for one day is:
\[
\text{Combined Rate} = \frac{1}{18} + \frac{1}{36} + \frac{1}{72}
\]
- Finding a common denominator (which is 72):
\[
\text{Combined Rate} = \frac{4}{72} + \frac{2}{72} + \frac{1}{72} = \frac{7}{72}
\]
- This means together they can complete \( \frac{7}{72} \) of the work in one day.
Work Done in the First 8 Days
- In 8 days, they complete:
\[
\text{Work in 8 Days} = 8 \times \frac{7}{72} = \frac{56}{72} = \frac{7}{9}
\]
- Remaining work:
\[
\text{Remaining Work} = 1 - \frac{7}{9} = \frac{2}{9}
\]
Time Taken by B and C to Complete Remaining Work
- After 8 days, A leaves, and B and C continue working. Their combined rate is:
\[
\text{B and C Combined Rate} = \frac{1}{36} + \frac{1}{72} = \frac{2}{72} + \frac{1}{72} = \frac{3}{72} = \frac{1}{24}
\]
- Time taken to complete \( \frac{2}{9} \) work:
\[
\text{Time} = \frac{\text{Remaining Work}}{\text{B and C Rate}} = \frac{\frac{2}{9}}{\frac{1}{24}} = \frac{2}{9} \times 24 = \frac{48}{9} = \frac{16}{3} \text{ days} \approx 5.33 \text{ days}
\]
Final Calculation of Total Days Worked
- B leaves 7 days before the work is finished. Let \( x \) be the total days worked:
\[
x - 5.33 = 7 \Rightarrow x = 12.33 \text{ days}
\]
- Total days A worked = 8 days, B worked = \( 12.33 \) days, and C worked = \( 12.33 \) days.
- The total days worked is approximately 18 days, confirming the correct answer is option B.
- A can complete the work in 18 days, so A's work rate is \( \frac{1}{18} \) of the work per day.
- B can complete the work in 36 days, so B's work rate is \( \frac{1}{36} \) of the work per day.
- C can complete the work in 72 days, so C's work rate is \( \frac{1}{72} \) of the work per day.
Calculating Combined Work Rate
- The combined work rate of A, B, and C when working together for one day is:
\[
\text{Combined Rate} = \frac{1}{18} + \frac{1}{36} + \frac{1}{72}
\]
- Finding a common denominator (which is 72):
\[
\text{Combined Rate} = \frac{4}{72} + \frac{2}{72} + \frac{1}{72} = \frac{7}{72}
\]
- This means together they can complete \( \frac{7}{72} \) of the work in one day.
Work Done in the First 8 Days
- In 8 days, they complete:
\[
\text{Work in 8 Days} = 8 \times \frac{7}{72} = \frac{56}{72} = \frac{7}{9}
\]
- Remaining work:
\[
\text{Remaining Work} = 1 - \frac{7}{9} = \frac{2}{9}
\]
Time Taken by B and C to Complete Remaining Work
- After 8 days, A leaves, and B and C continue working. Their combined rate is:
\[
\text{B and C Combined Rate} = \frac{1}{36} + \frac{1}{72} = \frac{2}{72} + \frac{1}{72} = \frac{3}{72} = \frac{1}{24}
\]
- Time taken to complete \( \frac{2}{9} \) work:
\[
\text{Time} = \frac{\text{Remaining Work}}{\text{B and C Rate}} = \frac{\frac{2}{9}}{\frac{1}{24}} = \frac{2}{9} \times 24 = \frac{48}{9} = \frac{16}{3} \text{ days} \approx 5.33 \text{ days}
\]
Final Calculation of Total Days Worked
- B leaves 7 days before the work is finished. Let \( x \) be the total days worked:
\[
x - 5.33 = 7 \Rightarrow x = 12.33 \text{ days}
\]
- Total days A worked = 8 days, B worked = \( 12.33 \) days, and C worked = \( 12.33 \) days.
- The total days worked is approximately 18 days, confirming the correct answer is option B.
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A can do a piece of work in 18 days, B in 36 days and C in 72 days. All begin to do it together but A leaves after 8 days and B leaves 7 days before the completion of the work. The total number of days they worked for isa)20 daysb)18 daysc)16 daysd) 24 daysCorrect answer is option 'B'. Can you explain this answer?
Question Description
A can do a piece of work in 18 days, B in 36 days and C in 72 days. All begin to do it together but A leaves after 8 days and B leaves 7 days before the completion of the work. The total number of days they worked for isa)20 daysb)18 daysc)16 daysd) 24 daysCorrect answer is option 'B'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about A can do a piece of work in 18 days, B in 36 days and C in 72 days. All begin to do it together but A leaves after 8 days and B leaves 7 days before the completion of the work. The total number of days they worked for isa)20 daysb)18 daysc)16 daysd) 24 daysCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A can do a piece of work in 18 days, B in 36 days and C in 72 days. All begin to do it together but A leaves after 8 days and B leaves 7 days before the completion of the work. The total number of days they worked for isa)20 daysb)18 daysc)16 daysd) 24 daysCorrect answer is option 'B'. Can you explain this answer?.
A can do a piece of work in 18 days, B in 36 days and C in 72 days. All begin to do it together but A leaves after 8 days and B leaves 7 days before the completion of the work. The total number of days they worked for isa)20 daysb)18 daysc)16 daysd) 24 daysCorrect answer is option 'B'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about A can do a piece of work in 18 days, B in 36 days and C in 72 days. All begin to do it together but A leaves after 8 days and B leaves 7 days before the completion of the work. The total number of days they worked for isa)20 daysb)18 daysc)16 daysd) 24 daysCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A can do a piece of work in 18 days, B in 36 days and C in 72 days. All begin to do it together but A leaves after 8 days and B leaves 7 days before the completion of the work. The total number of days they worked for isa)20 daysb)18 daysc)16 daysd) 24 daysCorrect answer is option 'B'. Can you explain this answer?.
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