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A is twice efficient as B. A and B together do the same work in as much time as C and D can do together. If the ratio of the number of alone working days of C to D is 2:3 and if B worked 16 days more than C then no of days which A worked alone?
- a)18 Days
- b)20 Days
- c)30 Days
- d)36 Days
- e)Cannot be determined
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A is twice efficient as B. A and B together do the same work in as muc...
The ratio of efficiencies of A and B = 2 : 1
Then the ratio of the number of days taken by A and B will be 1 : 2 (∵ Time is inversely proportional to efficiency)
Let the working days for A, B, C, and D are,
A = x, B = 2x, C = 2y, D = 3y
Now, 1/x + 1/2x = 1/2y + 1/3y
⇒ 3/2x = 5/6y
⇒ 18y = 10x
⇒ x : y = 9 : 5
And 2x – 2y = 16
Now, solving both the equations, we get,
⇒ x = 18 days.
∴Number of days which A worked alone is 18 days.
Most Upvoted Answer
A is twice efficient as B. A and B together do the same work in as muc...
Given:
- A is twice efficient as B.
- A and B together do the same work in as much time as C and D can do together.
- The ratio of the number of alone working days of C to D is 2:3.
- B worked 16 days more than C.
To find:
- The number of days which A worked alone.
Solution:
Let's assume that B can do a work of 1 unit in x days. So, A can do a work of 2 units in x days.
Therefore, efficiency of A and B can be written as:
- A = 2/x
- B = 1/x
Now, A and B together can do a work of 3 units in the same time as C and D can do together. Let's assume that C can do a work of y units in 1 day, so D can do a work of (3y/2) units in 1 day.
Therefore, efficiency of C and D can be written as:
- C = y/1 = y
- D = (3y/2)/1 = (3y/2)
Now, let's assume that C worked for z days alone. So, D worked for (3z/2) days alone.
Given that the ratio of the number of alone working days of C to D is 2:3. So, we can write:
- z/(3z/2) = 2/3
Solving this equation, we get:
- z = 6
Therefore, C can do a work of 6y units alone in 6 days and D can do a work of 9y units alone in 9 days.
Also, given that B worked 16 days more than C. So, if C worked for z days alone, then B worked for (z+16) days alone.
Therefore, B can do a work of (z+16) units alone in (z+16) days, which is equal to the work done by A alone.
Now, we can equate the work done by A and B alone to get:
- 2/x * d = (z+16)/x
where d is the number of days A worked alone.
Solving this equation for d, we get:
- d = 18 days
Therefore, the number of days which A worked alone is 18 days. Hence, option (a) is the correct answer.
- A is twice efficient as B.
- A and B together do the same work in as much time as C and D can do together.
- The ratio of the number of alone working days of C to D is 2:3.
- B worked 16 days more than C.
To find:
- The number of days which A worked alone.
Solution:
Let's assume that B can do a work of 1 unit in x days. So, A can do a work of 2 units in x days.
Therefore, efficiency of A and B can be written as:
- A = 2/x
- B = 1/x
Now, A and B together can do a work of 3 units in the same time as C and D can do together. Let's assume that C can do a work of y units in 1 day, so D can do a work of (3y/2) units in 1 day.
Therefore, efficiency of C and D can be written as:
- C = y/1 = y
- D = (3y/2)/1 = (3y/2)
Now, let's assume that C worked for z days alone. So, D worked for (3z/2) days alone.
Given that the ratio of the number of alone working days of C to D is 2:3. So, we can write:
- z/(3z/2) = 2/3
Solving this equation, we get:
- z = 6
Therefore, C can do a work of 6y units alone in 6 days and D can do a work of 9y units alone in 9 days.
Also, given that B worked 16 days more than C. So, if C worked for z days alone, then B worked for (z+16) days alone.
Therefore, B can do a work of (z+16) units alone in (z+16) days, which is equal to the work done by A alone.
Now, we can equate the work done by A and B alone to get:
- 2/x * d = (z+16)/x
where d is the number of days A worked alone.
Solving this equation for d, we get:
- d = 18 days
Therefore, the number of days which A worked alone is 18 days. Hence, option (a) is the correct answer.
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A is twice efficient as B. A and B together do the same work in as much time as C and D can do together. If the ratio of the number of alone working days of C to D is 2:3 and if B worked 16 days more than C then no of days which A worked alone?a)18 Daysb)20 Daysc)30 Daysd)36 Dayse)Cannot be determinedCorrect answer is option 'A'. Can you explain this answer?
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