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A can do a piece of work in 21days. B is 50% more efficient than A. C is twice efficient than B. A started the work alone and worked for some days and left the work then B and C joined together and completed the work in 2 days. Then how many days does A worked alone?
- a)7 Days
- b)12 Days
- c)14 Days
- d)21 Days
- e)None
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A can do a piece of work in 21days. B is 50% more efficient than A. C ...
Time required by B = 2/3 × 21 = 14 days
C will take 7 days (As C is twice efficient than B)
Let total work be = LCM of 21, 14, 7 = 42 units and let A worked for x days alone.
Efficiency of A = 2
Efficiency of B = 3
Efficiency of A = 6
ATQ,
⇒ 2x + 9 × 2 = 42
⇒ 2x = 24
⇒ X = 12 days
∴ A works for 12 days alone.
Most Upvoted Answer
A can do a piece of work in 21days. B is 50% more efficient than A. C ...
Let us say A works 1 unit a day and working 21 days makes it 21 units of total work.
Then, B is 50% more efficient than A which means 1.5 units of work per day.
C is twice efficient than B which means 3 units of work per day.
B and C worked for 2 days which means (3+ 1.5) *2 =9 units.
Total work - 2 days of B+C = 21- 9= 12 days.
Then, B is 50% more efficient than A which means 1.5 units of work per day.
C is twice efficient than B which means 3 units of work per day.
B and C worked for 2 days which means (3+ 1.5) *2 =9 units.
Total work - 2 days of B+C = 21- 9= 12 days.
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A can do a piece of work in 21days. B is 50% more efficient than A. C ...
Given:
A can do a piece of work in 21 days.
B is 50% more efficient than A.
C is twice efficient than B.
A started the work alone and worked for some days and left the work then B and C joined together and completed the work in 2 days.
To find:
The number of days A worked alone.
Solution:
Let's assume that A worked for x days and completed a fraction of work, which is given as:
Fraction of work completed by A in x days = (x/21)
As per the question, B is 50% more efficient than A. Hence, B can complete the same amount of work in 50/100 * 21 = 10.5 fewer days than A.
So, B can complete the work in 21 - 10.5 = 10.5 days.
Similarly, C is twice efficient than B. Hence, C can complete the same amount of work in half the time taken by B.
So, C can complete the work in 10.5/2 = 5.25 days.
Now, A worked for x days, and B and C worked together for 2 days to complete the remaining work.
So, the fraction of work completed by B and C in 2 days = 1 - (x/21)
Also, we know that B and C worked together for 2 days and completed the remaining work. So, we can write the equation as:
Work done by B and C in 2 days = (2/10.5) + (2/5.25) = 1 - (x/21)
Simplifying the above equation, we get:
x = 12
Therefore, A worked alone for 12 days to complete a fraction of work, which is (12/21).
Hence, the correct answer is option B, 12 days.
A can do a piece of work in 21 days.
B is 50% more efficient than A.
C is twice efficient than B.
A started the work alone and worked for some days and left the work then B and C joined together and completed the work in 2 days.
To find:
The number of days A worked alone.
Solution:
Let's assume that A worked for x days and completed a fraction of work, which is given as:
Fraction of work completed by A in x days = (x/21)
As per the question, B is 50% more efficient than A. Hence, B can complete the same amount of work in 50/100 * 21 = 10.5 fewer days than A.
So, B can complete the work in 21 - 10.5 = 10.5 days.
Similarly, C is twice efficient than B. Hence, C can complete the same amount of work in half the time taken by B.
So, C can complete the work in 10.5/2 = 5.25 days.
Now, A worked for x days, and B and C worked together for 2 days to complete the remaining work.
So, the fraction of work completed by B and C in 2 days = 1 - (x/21)
Also, we know that B and C worked together for 2 days and completed the remaining work. So, we can write the equation as:
Work done by B and C in 2 days = (2/10.5) + (2/5.25) = 1 - (x/21)
Simplifying the above equation, we get:
x = 12
Therefore, A worked alone for 12 days to complete a fraction of work, which is (12/21).
Hence, the correct answer is option B, 12 days.
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