B takes 16days less than A to do a piece of work. If both working together can do it in 15days, in how many days will B alone complete the work.
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Answer:
24 days
Step-by-step explanation:
Let work done by A = x days
therefore,
the work done by B= x-16(as per que.)
Together work done =15 days(given)
work done in one day,
\binom{1}{x} + \binom{1}{x - 16} = \binom{1}{15}
\frac{(x - 16) + x}{(x)(x - 16)} = \frac{1}{15}
\frac{2x - 16}{ {x}^{2} - 16x} = \frac{1}{15}
30x - 240 = {x}^{2} - 16x \\ {x}^{2} - 16x - 30x + 240 = 0 \\ {x}^{2} - 46x + 240 = 0 \\ \\ {x}^{2} - 40 x - 6x + 240 = 0 \\ x(x - 40) - 6(x - 40) = 0 \\ x = 6 \: or \: x = 40 \\ 6 \: is \: not \: possible \: beacause \: days \: are \: never \: negative \\ therefore. \\ days \: taken \: by \: a = 40days \\ and \: days \: taken \: by \: b \: is \: 40 - 16 = 24days
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