Question 884691

If one man or two women or three boys can finish a work in 66days then how many days will one man, one woman and one boy together take to finish the same work?
<pre>
Since 1 man can do the work in 66 days, he can do {{{1/66}}} of work in 1 day
Since 2 women can do the work in 66 days, then 1 woman can do work in 2(66), or 132 days, or {{{1/132}}} of work in 1 day
Since 3 boys can do the work in 66 days, then 1 boy can do work in 3(66), or 198 days, or {{{1/198}}} of work in 1 day
Therefore, with T being time it’ll take 1 man, 1 woman, and 1 boy, we have:
{{{(1/66 + 1/132 + 1/198)/1 = 1/T}}}
{{{1/66 + 1/132 + 1/198 = 1/T}}}
6T + 3T + 2T = 396 ------- Multiplying by LCD, 396T
11T = 396 ------- Cross-multiplying
T, or time taken by 1 man, 1 woman, and 1 boy to complete the work = {{{396/11}}}, or {{{highlight_green(highlight_green(36))}}} days
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