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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 information:
- 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.
- B and C joined together and completed the work in 2 days.
To find: How many days did A work alone?
Step-by-step solution:
Let's assume that A worked alone for x days.
Efficiency of A = 1/21
Efficiency of B = 1.5 x (1/21) = 1/14
Efficiency of C = 2 x (1/14) = 1/7
Now, let's consider the work done by each person:
- A worked alone for x days, so the work done by A = (1/21) x (x) = x/21
- After A left, B and C joined together and completed the remaining work in 2 days.
- Let's assume that B and C worked together for y days to complete the remaining work.
- So, the work done by B and C together = (1/14 + 1/7) x (y) = (3/14) x (y) = 3y/42 = y/14
- Total work done by A and B and C together = 1 (i.e., the whole work is completed)
Using the above information, we can form the equation:
x/21 + y/14 = 1
We know that B and C completed the remaining work in 2 days, so
(1/14 + 1/7) x (2) = (3/14) x (2) = 3/7 work is completed by B and C together in 2 days.
Now, we can form another equation using the above information:
y/14 = 3/7
y = 6
Substitute y = 6 in the first equation to find x:
x/21 + 6/14 = 1
x/21 = 1/2
x = 21/2 = 10.5
Therefore, A worked alone for 10.5 days, which is approximately equal to 12 days.
Hence, option B is the correct answer.
- 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.
- B and C joined together and completed the work in 2 days.
To find: How many days did A work alone?
Step-by-step solution:
Let's assume that A worked alone for x days.
Efficiency of A = 1/21
Efficiency of B = 1.5 x (1/21) = 1/14
Efficiency of C = 2 x (1/14) = 1/7
Now, let's consider the work done by each person:
- A worked alone for x days, so the work done by A = (1/21) x (x) = x/21
- After A left, B and C joined together and completed the remaining work in 2 days.
- Let's assume that B and C worked together for y days to complete the remaining work.
- So, the work done by B and C together = (1/14 + 1/7) x (y) = (3/14) x (y) = 3y/42 = y/14
- Total work done by A and B and C together = 1 (i.e., the whole work is completed)
Using the above information, we can form the equation:
x/21 + y/14 = 1
We know that B and C completed the remaining work in 2 days, so
(1/14 + 1/7) x (2) = (3/14) x (2) = 3/7 work is completed by B and C together in 2 days.
Now, we can form another equation using the above information:
y/14 = 3/7
y = 6
Substitute y = 6 in the first equation to find x:
x/21 + 6/14 = 1
x/21 = 1/2
x = 21/2 = 10.5
Therefore, A worked alone for 10.5 days, which is approximately equal to 12 days.
Hence, option B is the correct answer.
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