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A, B and C can complete a work in 20 days working together. A and B together are 50% more efficient than C and A & C together are 100% more efficient than B. Then in how many days A alone can complete the work?
- a)None of these
- b)85 days
- c)80 days
- d)75 days
- e)65 days
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A, B and C can complete a work in 20 days working together. A and B to...
Let efficiency of A, B and C be a, b and c respectively
ATQ,
On solving (i) and (ii)
ATQ,
On solving (i) and (ii)
a : b : c = 4 : 5 : 6
∴ A alone can complete in
=75 days
∴ A alone can complete in
=75 daysMost Upvoted Answer
A, B and C can complete a work in 20 days working together. A and B to...
If A, B, and C can complete a work in 20 days working together, it means that their combined efficiency is such that they can complete 1/20th of the work in a day. Let's assume the efficiency of A, B, and C individually is represented by a, b, and c, respectively.
So, we have the equation:
1/20 = a + b + c
Now, let's consider the second statement that A and B together are 50% more efficient than C and A. This means that the combined efficiency of A and B is 1.5 times the combined efficiency of C and A. Mathematically, we can represent this as:
a + b = 1.5(a + c)
Expanding the equation:
a + b = 1.5a + 1.5c
Rearranging the terms:
0.5a = 0.5c
Dividing both sides by 0.5:
a = c
Substituting this value in the first equation:
1/20 = a + b + a
1/20 = 2a + b
Now, we can solve these equations simultaneously to find the values of a, b, and c.
Substituting a = c:
1/20 = 2a + b
1/20 = 2a + a
1/20 = 3a
a = 1/60
Substituting the value of a in the equation a + b = 1.5(a + c):
1/60 + b = 1.5(1/60 + 1/60)
1/60 + b = 1.5/60 + 1.5/60
1/60 + b = 3/60
b = 2/60
Simplifying the fractions:
b = 1/30
Finally, substituting the values of a and b in the equation 1/20 = a + b + c:
1/20 = 1/60 + 1/30 + c
1/20 = 3/60 + 2/60 + c
1/20 = 5/60 + c
1/20 - 5/60 = c
3/60 = c
c = 1/20
Therefore, the efficiency of A, B, and C individually is:
a = 1/60
b = 1/30
c = 1/20
So, we have the equation:
1/20 = a + b + c
Now, let's consider the second statement that A and B together are 50% more efficient than C and A. This means that the combined efficiency of A and B is 1.5 times the combined efficiency of C and A. Mathematically, we can represent this as:
a + b = 1.5(a + c)
Expanding the equation:
a + b = 1.5a + 1.5c
Rearranging the terms:
0.5a = 0.5c
Dividing both sides by 0.5:
a = c
Substituting this value in the first equation:
1/20 = a + b + a
1/20 = 2a + b
Now, we can solve these equations simultaneously to find the values of a, b, and c.
Substituting a = c:
1/20 = 2a + b
1/20 = 2a + a
1/20 = 3a
a = 1/60
Substituting the value of a in the equation a + b = 1.5(a + c):
1/60 + b = 1.5(1/60 + 1/60)
1/60 + b = 1.5/60 + 1.5/60
1/60 + b = 3/60
b = 2/60
Simplifying the fractions:
b = 1/30
Finally, substituting the values of a and b in the equation 1/20 = a + b + c:
1/20 = 1/60 + 1/30 + c
1/20 = 3/60 + 2/60 + c
1/20 = 5/60 + c
1/20 - 5/60 = c
3/60 = c
c = 1/20
Therefore, the efficiency of A, B, and C individually is:
a = 1/60
b = 1/30
c = 1/20
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A, B and C can complete a work in 20 days working together. A and B together are 50% more efficient than C and A & C together are 100% more efficient than B. Then in how many days A alone can complete the work?a)None of theseb)85 daysc)80 daysd)75 dayse)65 daysCorrect answer is option 'D'. Can you explain this answer?
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