2 workers A and B working together completed a job in 5 days. If A worked twice as efficiently as he actually did and B worked 1/3rd as efficiently as he actually did, the work would have been completed in 3 days. A alone could complete the work in:
A 21/4 days
B 25/4 days
C 15/2 days
D 75/8 days
E none of these
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vaibhav101
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Let the job = 15 units.vaibhav101 wrote:2 workers A and B working together completed a job in 5 days. If A worked twice as efficiently as he actually did and B worked 1/3rd as efficiently as he actually did, the work would have been completed in 3 days. A alone could complete the work in:
A 21/4 days
B 25/4 days
C 15/2 days
D 75/8 days
E none of these
Since A and B take 5 days to produce the 15-unit job, A+B = w/t = 15/5 = 3 units per day.
Thus:
A+B = 3.
Since 2A and (1/3)B take 3 days to produce the 15-unit job, 2A + (1/3)B = w/t = 15/3 = 5 units per day.
Thus:
2A + (1/3)B = 5
6A + B = 15.
Subtracting the red equation from the blue equation, we get:
(6A + B) - (A+B) = 15 - 3
5A = 12
A = 12/5 units per day.
Since A's rate = 12/5 units per day, the time for A alone to produce the 15-unit job = 15/(12/5) = 75/12 = 25/4 days.
The correct answer is B.
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The rate of A is 1/A and the rate of B is 1/B.vaibhav101 wrote:2 workers A and B working together completed a job in 5 days. If A worked twice as efficiently as he actually did and B worked 1/3rd as efficiently as he actually did, the work would have been completed in 3 days. A alone could complete the work in:
A 21/4 days
B 25/4 days
C 15/2 days
D 75/8 days
E none of these
If A works twice as efficiently, the new rate is 1/A x 2 = 2/A
The new rate of B is 1/3 x 1/B = 1/(3B)
So we have two equations:
1/A + 1/B = 1/5
Multiplying by 2, we have:
2/A + 2/B = 2/5
and
2/A + 1/(3B) = 1/3
Subtracting the 2nd equation from the first, we have:
2/B - 1/(3B) = 2/5 - 1/3
Multiplying by 15B, we have:
30 - 5 = 6B - 5B
25 = B
Let's now determine A:
1/A + 1/25 = 1/5
Multiplying by 25A, we have:
25 + A = 5A
25 = 4A
25/4= A
Answer: B
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