Question

A can build a wall in the same time in which B and C together can do it. If A and B together could do it in 25 days and C alone in 35 days, in what time could B alone do it?A. 175 daysB. 100 daysC. 90 daysD. None of these

Answer 1

175 will be the answer

Answer 2

$( A + B)'s \: 1 \: day's \: work = \frac{ 1}{25}$

$C's \: 1 \: day's \:work = \frac{1}{35}$

$( A+B+C)'s \: 1 \:day's \: work\\ = \Big( \frac{1}{25} + \frac{1}{35} \Big) \\= \frac{ 7 + 5 }{175} \\= \frac{12}{175} \: ---(1)$

/* According to the problem given */

$A's \: 1 \:day's \:work \\= ( B + C)'s \: 1 \: day's \:work\: --(2)$

/* From (1) and (2), we get */

$2 \times ( A's \: 1 \:day \:work ) = \frac{12}{175}$

$\implies A's \: 1 \:day \:work \\= \frac{12}{175\times 2} \\= \frac{6}{175}$

$\therefore B's \: 1 \:day \: work \\= \Big( \frac{1}{25} - \frac{6}{175} \Big) \\= \frac{ 7 - 6}{175} \\= \frac{1}{175}$

$So, B \: alone \: could \: do \:the \:work \: in \\175 \: days .$

Therefore.,

$Option \: \pink { (A) } \: is \: correct .$

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