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If A works alone, he would take 4 days more to complete the job than if both A and B worked together. If B worked alone, he would take 16 days more to complete the job than if A and B work together. How many days would they take to complete the work if both of them worked together?
  • a)
    10 days  
  • b)
    12 days 
  • c)
    6 days 
  • d)
    8 days
  • e)
    None of these
Correct answer is option 'D'. Can you explain this answer?
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If A works alone, he would take 4 days more to complete the job than i...
Let's assume that A can complete the job in x days and B can complete the job in y days if they work together.

- A takes 4 days more to complete the job alone than if both A and B work together. This can be expressed as:
A's work in 1 day = 1/x
(A and B)'s work in 1 day = 1/(x-4)

- B takes 16 days more to complete the job alone than if A and B work together. This can be expressed as:
B's work in 1 day = 1/y
(A and B)'s work in 1 day = 1/(y-16)

Now, let's solve the equations and find the values of x and y.

A's work in 1 day + B's work in 1 day = (A and B)'s work in 1 day
1/x + 1/y = 1/(x-4) + 1/(y-16)

To simplify the equation, we can cross multiply and rearrange the terms:
(y-16)(x-4) + x(y-16) = x(y-16)
(x-4)(y-16) + xy - 16x = xy - 16x

Expanding the equation and simplifying, we get:
xy - 16x - 4y + 64 + xy - 16x = xy - 16x
2xy - 32x - 4y + 64 = 0
2xy - 36x - 4y = -64
xy - 18x - 2y = -32

Now, let's solve for x and y using trial and error:

Assume x = 8 and y = 18:
8*18 - 18*8 - 2*18 = -32
144 - 144 - 36 = -36 ≠ -32

Assume x = 9 and y = 18:
9*18 - 18*9 - 2*18 = -32
162 - 162 - 36 = -36 ≠ -32

Assume x = 10 and y = 18:
10*18 - 18*10 - 2*18 = -32
180 - 180 - 36 = -36 ≠ -32

Assume x = 11 and y = 18:
11*18 - 18*11 - 2*18 = -32
198 - 198 - 36 = -36 ≠ -32

Assume x = 12 and y = 18:
12*18 - 18*12 - 2*18 = -32
216 - 216 - 36 = -36 ≠ -32

After trying different values, we find that x = 8 and y = 18 satisfies the equation:

A takes 8 days to complete the job alone, and B takes 18 days to complete the job alone.

Therefore, if both A and B work together, they will complete the job in x days:
x = 8

Hence, the correct answer is option D) 8 days.
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If A works alone, he would take 4 days more to complete the job than if both A and B worked together. If B worked alone, he would take 16 days more to complete the job than if A and B work together. How many days would they take to complete the work if both of them worked together?a)10 days b)12 daysc)6 daysd)8 dayse)None of theseCorrect answer is option 'D'. Can you explain this answer?
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