Question 15

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?

Solution

let A and B together complete the work in x days

time taken by A = (x + 4) days

time taken by B = (x + 16) days

therefore $$ \frac{1}{x + 4} + \frac{1}{x + 16} = \frac{1}{x} $$

$$ \frac{x + 16 + x + 4}{(x + 4)(x + 16)} = \frac{1}{x} $$

$$ \frac{2x + 20}{x^2 + 16x + 4x + 64} = \frac{1}{x} $$

$$ \frac{2x + 20}{x^2 + 20x + 64} = \frac{1}{x} $$

$$ 2x^2 + 20x = x^2 + 20x + 64 $$

$$ x^2 = 64 $$

x = 8 days

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