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A, B and C together can complete a work in 8 days. If A is 50% more efficient than B and B is 50% less efficient than C, then B alone will complete the same work in:
- a)16 days
- b)24 days
- c)48 days
- d)36 days
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A, B and C together can complete a work in 8 days. If A is 50% more ef...
Solution:
Let's assume that C can complete the work in x days.
Efficiency of B compared to C:
B is 50% less efficient than C. This means B can complete only half the work that C can complete in the same time. So, B can complete the work in 2x days.
Efficiency of A compared to B:
A is 50% more efficient than B. This means A can complete 1.5 times the work that B can complete in the same time. So, A can complete the work in (2x/1.5) days.
Efficiency of A, B, and C together:
Given that A, B, and C together can complete the work in 8 days. So, their combined efficiency is 1/8 of the work per day.
Let's calculate their combined efficiency:
1/A + 1/B + 1/C = 1/8
Substituting the values of A, B, and C:
1/(2x/1.5) + 1/2x + 1/x = 1/8
Taking the LCM and simplifying the equation:
[(1.5 + 3 + 4)/2x] = 1/8
8/2x = 1/8
2x = 64
x = 32
So, C alone can complete the work in 32 days.
Now, let's find out how many days B alone will take to complete the work:
B can complete the work in 2x days.
Substituting the value of x:
B can complete the work in 2(32) = 64 days.
Therefore, the correct answer is option D) 36 days.
Let's assume that C can complete the work in x days.
Efficiency of B compared to C:
B is 50% less efficient than C. This means B can complete only half the work that C can complete in the same time. So, B can complete the work in 2x days.
Efficiency of A compared to B:
A is 50% more efficient than B. This means A can complete 1.5 times the work that B can complete in the same time. So, A can complete the work in (2x/1.5) days.
Efficiency of A, B, and C together:
Given that A, B, and C together can complete the work in 8 days. So, their combined efficiency is 1/8 of the work per day.
Let's calculate their combined efficiency:
1/A + 1/B + 1/C = 1/8
Substituting the values of A, B, and C:
1/(2x/1.5) + 1/2x + 1/x = 1/8
Taking the LCM and simplifying the equation:
[(1.5 + 3 + 4)/2x] = 1/8
8/2x = 1/8
2x = 64
x = 32
So, C alone can complete the work in 32 days.
Now, let's find out how many days B alone will take to complete the work:
B can complete the work in 2x days.
Substituting the value of x:
B can complete the work in 2(32) = 64 days.
Therefore, the correct answer is option D) 36 days.
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Community Answer
A, B and C together can complete a work in 8 days. If A is 50% more ef...
Let the efficiency of C be 10 units a day.
B's efficiency = 10 - 10 × 50% = 5 units
A's efficiency = 5 + 5 × 50% = 7.5 units
So, the total work = 8 × (10 + 5 + 7.5)
⇒ 8 × 22.5 = 180 units
Now, B alone will complete the work in = 180/5
⇒ 36 days
∴ B alone will complete the work in 36 days.
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A, B and C together can complete a work in 8 days. If A is 50% more efficient than B and B is 50% less efficient than C, then B alone will complete the same work in:a)16 daysb)24 daysc)48 daysd)36 dayse)None of theseCorrect answer is option 'D'. Can you explain this answer?
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